As I said and Phaedrus quoted, only taking Actions provokes AoO's.
If your DM wants to use Fluff text for RAW text, that's fine, he still loses.
"Sometimes a combatant in a melee lets her guard down. In this case, combatants near her can take advantage of her lapse in defense to attack her for free. These free attacks are called attacks of opportunity. "
Ok, *when* can someone take an AoO? "In this case..." What case? When you let your guard down. What is letting your guard down called, RAW? There is specific rules terminology for this situation; you can take an AoO if an AoO was *provoked*. The rules give a list of things that *provoke* AoOs; falling prone is not one of them, in fact, dropping to the floor as a Free Action is listed as specifically *not* provoking - although I understand your DMs argument that you're not dropping as a Free Action if it's on someone else's turn. But see, look at the chart. See under "No Action". See 5 ft step? That does not provoke either. I don't see why Falling can't be under "No Action", also look a subscript 1. This additionally reinforces the fact that falling prone, regardless of the action type, does not provoke. It's right there in the PHB pg. 141.
Additionally, only moving OUT of a threatened square provokes. Falling inside a 5ft square is CLEARLY not moving OUT of the square; it's movement within the square itself. Your DM has no legs to stand on.
Where in the rules does it say Falling Prone on someone else's turn is an Immediate Action or anything of the sort?
Anything else is a house-rule. Chart 8-2 is also very clear on this.