>... fluoride ion is the most basic ion, because it has the smallest size and thus the highest electron density.

A look at the Periodic table and the [ionization energies](https://en.wikipedia.org/wiki/Ionization_energy) is always a good idea to see what’s going on.

 1. The highest energies, required to remove an electron from the atom, are needed for the Noble gases. That means they are most aggressively reclaiming a removed electron back.
[![First ionization energies of elements][1]][1]

 2. The less the number of electrons around the nucleus of Noble gases, the higher the aggressiveness to retrieval a lost electron.

 3. The elements in the column before the Noble gases ($\ce {Fl}, {CL}, {Br}, ...$) are doing the same in an attenuated way. And more than that, in bounds these elements try to complete their electron shell to the Noble gas configuration.

Take the [Noble gas compounds](https://en.wikipedia.org/wiki/Noble_gas_compound). Fluor is able to remove electrons from Xenon:

[![All images from WP][2]][2]

The tendency to fulfill the electron configuration is higher for Fluor when the tendency for Xenon to preserve its electron configuration. The [Octet rule](https://en.wikipedia.org/wiki/Octet_rule) works better for elements with high ionization Energie when for elements with less ionization energies. (Perhaps instead of ionization energy in this case we have to remember the [electron affinity](https://en.wikipedia.org/wiki/Electron_affinity), but this seems to me to be more a scholastic difference in definition.) according the above image Fluor has a ionization energy of roughly 17 eV, Xenon has about 13 eV. That is why the octet rule in this case “works” for Fluor and against Xenon.

  [1]: https://i.sstatic.net/jkJFL.jpg
  [2]: https://i.sstatic.net/SyZers.jpg