It's probably to help keep the helium cold. Since you already have to maintain a large reservoir of a cryogenic fluid, why not make it do a little extra work to cool a substance with a lower boiling point.
It's probably inside for mechanical reasons pumping liquid helium is a nightmare it sips through pretty much everything (it can even go through glass when sufficiently cooled), in this case you don't really need to worry about all that stuff since you simply let the helium out and the difference in density would sort everything.
As for the reason it's not used to "cool the helium" it's because helium boils at -268.9c the liquid oxygen is cooled to -182.9c or to ~-206c in cryogenic mode, this is still way above the boiling temperature of helium. This would be about as effective at cooling, as cooling boiling oil with boiling water, incidentally it's also about as explosive ;)
For an ideal gas, PV = NkT, where P is pressure, V is volume, N is the number of atoms, T is temperature, and k is a constant. It looks like the O2 temperature for this version of Falcon is 66 K. If we take T_out ~ 273 K just for the sake of the discussion,
N_in / N_out = T_out / T_in ~ 4.
It's a significant difference.
Ideal gas law doesn't apply to real gasses, (actually in some cases especially helium).
Ideal gas law does not apply to liquids.
Ideal gas law only works at low pressure and high temperatures.
Overall the ideal gas law is not a law it's an approximation that works in a few cases, it has no baring in this case.
It can still somewhat behave as an ideal gas as low as 50K or so granted it is not under pressure.
Once you increase the pressure the ideal gas law breaks down pretty much completely, and is not applicable to liquid helium at about 6000PSI.
People also forget that the tank is made out usually titanium or aluminum (i think aluminum can't hold helium but am not sure about that) wrapped in a composite material usually Kevlar/Epoxy or some sort of carbon fiber composite, extreme low temperatures are well a bit tricky for these materials.
NASA had issues with that during the shuttle program, and it seems that even the new Orion has encountered issues with the effects of low temperature on COPV's which required them to develop new resins and composites http://www.compositesworld.com/articles/orion-composite-tank...
I'd be willing to bet it is to reduce the efficiency loss due to vacuum. The fuel tank (oxygen tank) is going to empty itself. However, you can't have a vacuum in the tank. So do you acknowledge that the rate of flow of fuel exiting the tank will be slowing down over time or do you keep the tank "full" to ensure constant pressure?
Helium, is inert, less dense than oxygen and cheap. It's probably the best space filling collection of atoms, and simultaneously it's density[1] forces the oxygen further "down"[0] the fuel tank.
[0] down is some direction relative to thrust. [1] density according to: "weight" generated by thrust.