ChemLibreTexts describes the radius ratio rule as follows.
(We) consider that the anion is the packing atom in the crystal and the
smaller cation fills interstitial sites ("holes"). Cations will find
arrangements in which they can contact the largest number of anions.
If the cation can touch all of its nearest neighbor anions, as shown
at the right for a small cation in contact with larger anions, then
the fit is good. If the cation is too small for a given site, that
coordination number will be unstable and it will prefer a lower
coordination structure.
Note that this interpretation allows for the radius of cation to be slightly larger spacing the anions out. This is depicted below.

Say the left and right limits of the ratio for stability limit ratio or critical ratio corresponding to maximum packing efficiency are $r_\text{min}$ and $r_\text{max}$, respectively. The (more) accurate interpretation of the radius ratio rule is:
$$
\dfrac{r_\text{cation}}{r_\text{anion}} \in [r_\text{min}, r_\text{max}+\epsilon)
$$
where $\epsilon$ is a small number. Now consider the octahedral (FCC) range.
$$
\dfrac{r_\text{cation}}{r_\text{anion}} \in \pu{[0.414, 0.732+\epsilon)}
$$
Since the radius ratio of $\ce{KCl}\ \pu{(0.735)}$ only differs from the upper limit of the octahedral coordination range by $\pu{0.003}$; therefore, it can show both FCC and BCC structures.
The radius ratio rule is really just a geometric rule, and, that too, a rule of thumb in solid-state chemistry. It helps make a priori predictions regarding the structures, that seem (mostly) work while making a bunch of assumptions and not considering a lot of factors. At the end of the day, the structure is what it is.
Some Assumptions of Radius Ratio Rules
- Ions are hard spheres.
- Only Electrostatic attraction occurs.
- Ions interact only to minimize electrostatic potential.
- No Polarization or Covalent bond formation occurs.
The list goes on...
If the assumptions of the radius ratio rule were accurate, square planer geometry shouldn't exist at all, because every square planer geometry can also exist as an octahedral one while minimizing electrostatic potential.
Do note that FCC to BCC phase transitions$^1$ of $\ce{KCl}$ have also been observed under (not too) high pressures ($\pu{GPa}$).
References
- Mashimo, Tsutomu & Nakamura, K & Tsumoto, K & Zhang, Y & Ando, Shinji & Tonda, H. (2002). Phase transition of KCl under shock compression. Journal of Physics: Condensed Matter. 14. 10783. 10.1088/0953-8984/14/44/377.