Summary: there is not necessarily a contradiction between the two.
- Radiation is not contagious, and
- a person who has been exposed to ionizing radiation is not dangerous to other people once they are not contaminated with radioactive material any more, but
- while they are still contaminated with radioactive material, they may pose a danger (highest danger is to themselves, though).
- In any case, other people are dangerous to someone who suffers radiation illness (infection risk).
Moreover,
- Thinking radiation contagious is (still!) a fairly widespread mistake, and
- I'd think misunderstanding the purpose of the instructions (she being dangerous for her husband rather than the other way round) quite likely in a highly stressful situations such as the husband dying. I.e., I wouldn't expect her to spend time then on double-checking whether she correctly understood the reason behind the instructions and ask, "Sorry, sister, is this because he's dangerous to me or because I'm dangerous to him?".
Thus, it should not be surprising to meet any such misconceptions in such a book. Nor would I be surprised if readers misunderstand the book this way even in case the firefighter's wife is and was perfectly aware that her husband did not pose a radiation danger to her. I'm writing the remainder of this answer mostly assuming that the mistake is in the book rather than on OP's side.
There are basically only two possibilities clear a misunderstanding that happened back then in a book of witness reports: the witness saying "nowadays I know I was dangerous to him, not he to me. But back then I didn't know that."
or the editor putting a footnote explaining the misunderstanding and that it was widespread at the time.
Ionizing radiation and contamination with radioactive substances
Radiation is not contagious in the sense that the firefighter's exposure to ionizing radiation did make him radiate himself. That being said,
But: chemical contamination, including radioactive substances, can be transferred from one body to another, and they can be incorporated and accumulated where they cause much damage.
(I also wouldn't call that contagious, since the total amount of radioactive material does not increase, but if you consider, say, crystal violet or methylene blue contagious "since if you touch someone, the ones touched by them will be violet/blue", then you can also call the radioactive substances contagious)
However, any radioactive substance contamination that is transferred to a practically relevant amount by touching can also be washed off - and that is the first thing to do for decontamination besides taking off potentially contaminated clothes. Any injury that means that the area cannot be thoroughly washed can also not be touched (for reason of the injury).
Thirdly, during the decay of such radioactive material, other substances form, which may be far more difficult to get rid of (see radon example below). Here, one may say that one can "catch" a contamination that one doesn't easily get rid off again. However, any such conamination would not be transferred from the firefighter to his wife.
X-rays/γ-rays: these are ionizing electromagnetic rays, i.e. high energy photons. They cause damage when being absorbed, either by directly damaging some biomolecule or by forming OH⋅ radicals/ROS which in turn cause further damage.
The radicals in themselves are nothing very special - they occur all the time as side products of our energy metabolism and we have powerful mechanisms to cope with them. Part of radiation illness is that these mechanisms are overwhelmed.
So, after exposure to X- or γ-rays, we have radicals inside the body, but no "foreign" nuclei, and no body surface contamination. I.e. nothing that became radioactive because of the exposure to high energy photons.
A somewhat different example related to Chernobyl and Fukushima would be incorporation of radioactive $\ce{^{131}I}$ in the thyroid gland. In particular, if someone with iodine deficiency incorporates iodine, pretty much all of it will end up in the thyroid gland. If that available iodine is $\ce{^{131}I}$, their thyroid gland will subsequently be exposed to large radiation doses. This incorporated radioactivity does include γ radiation of which a part leaves their body.
$\ce{^{131}I}$ is administered in radiotherapy in doses where the patients are e.g. kept in hospital for approximately 2 days (at least here in Germany) so as to not contaminate the wastewater with the radioactive $\ce{^{131}I}$ they excrete in their urine. Such patients are also advised to avoid close contact for e.g. a week after treatment in order to not cause accidental exposure to others, in particular children and pregnant women.. Such radiotherapy treatements use dosages in the 100 - 400 Gy range to the thyroid. And the guidelines are of course with a safety margin. A quick search for $\ce{^{131}I}$ radiation doeses to the thyroid in Ukrainian children after Chernobyl got me to Brenner et al: I‐131 Dose Response for Incident Thyroid Cancers in Ukraine Related to the Chornobyl Accident. The largst dose category is > 3.0 Gy, and a diagram has a point a bit below 5 Gy, so 1 - 2 orders of magnitude below the radiotherapy doses.
My conclusion from this is that even in case the firefighter got a $\ce{^{131}I}$ dose to kill off his thyroid, the wife giving the dying husband several close goodbye hugs 10 - 14 days after the exposure would be unlikely to pose a significant threat to her health due to radiation from his thyroid (and under the particular circumstances, the $\ce{^{131}I}$ she ingested after the accident would be a far more important concern for her health).
Again, I would not describe this as "contagious" - but your word use may vary.
In this guest post to cancer letter, R. P. Gale discusses some of his experiences as an MD at the famous hospital 6 (the Soviet Russian radiation clinic) treating the radiation illness patients from Chernobyl with at particular view to the HBO series.
Another error was to portray the victims as being dangerously radioactive. Most radiation contamination was superficial and relatively easily managed by routine procedures. This is entirely different than the Goiania accident, where the victims ate 137-cesium and we had to isolate them from most medical personnel.
Lastly, there is the dangerous representation that, because one of the victims was radioactive, his pregnant wife endangered her unborn child by entering his hospital room. First, as discussed, none of the victims were radioactive—their exposures were almost exclusively external, not internal. More importantly, risk to a fetus from an exposure like this is infinitesimally small.
Valid Reasons for not allowing the wife close to the husband that have nothing to do with radiation being "contagious".
Radiation illness: the bone marrow is rather radiation sensitive, and leukopenia (too low leukocyte counts, a type of immune suppression) are a typical part of radiation illness.
A radiation illness patient is thus at a very high risk from infections.
Radiation illness often comes with burns (the skin is most exposed, and for α and β radiation, almost all damage happens in the skin). Already "normal" severe burns are doubly difficult in terms of infections: the skin damage means that the normal protective barrier against microorganisms is broken down in those areas, and in addition there is a severe immune suppression (after initial inflammatory response). Infections cause half of the deaths after severe burns
Both are very valid safety reasons, just for the firefighter rather than for his wife's safety. Saying that the wife can go close to the firefighter would amount to saying "He's anyways going to die within the next days - it doesn't matter whether he catches an additional sepsis."
"Contagious" radiation as wrong but possibly valid concern after the Chernobyl accident
So from a scientific point of view radiation is not "contagious". Nevertheless, there is a still widespread, though mistaken fear of this. Personally, here and now I count this pretty much in the tin foil hat corner. But OTOH, in the situation in the Ukraine(ian SSR) immediately after the accident I think it a more understandable concern since the possibilities to check whether this concern is valid or not were severely limited. Not only for the general population, but even for the medical staff. In such a situation, it is a valid decision to err on the side of caution.
In addition: How much did the hospital staff know about what actually had happened and what the firefighter had actually been exposed to?
With those activities to hush up the Chernobyl incident, the hospital staff may have been unsure about what else that firefighter had been exposed to besides high doses of radiation.
Remaining contamination with radioactive material (including incorporated material) can be measured comparatively easily. However, I have no idea whether such instruments were available at the hospitals, say, in Kiev, to measure remaining contamination of their patients: a) the available instruements may have been needed more urgently at the site of the power plant and b) also political coniderations/hushing up may have been standing against that. I'd expect the Moskow hospital to have all kinds of instruments (but that may be my predjudice)
* I'm pretty sure that a non-negligible fraction of the population here in Germany would express that fear if you ask them. Including medical staff, and even after Chernobyl and Fukushima.
If you want an example: have a look at this post (in German) about radiation treatment for food on a web site by the offical consumer protection organizations
Werden Lebensmittel mit ionisierenden Strahlen behandelt, wird die Strahlenmenge genau dosiert. Die Energiemenge ist so gering, dass die Lebensmittel nicht radioaktiv werden und sich nur leicht erwärmen.
My translation and my emphasis:
When food is treated with ionizing radiation, the amount of radiation is accurately dosed. The energs is so small that the food does not become radioactive and only heats up slightly.
While it is of course true that the food does not become radioactive, that sentence IMHO does insinuate that this could [easily] be the case with higher doses. And one comment (out of a total of 14) clearly indictates that the writer thinks radiated potatoes will radiate themselves.
