"There is no direct rules quote that will ever truly answer the question… however, a simple logic problem can be used to answer it.
If you only count a large creature as leaving a square when it nolonger occupies said square then you create a situation where a creature can leave either 2 or 3 squares in one tile of movement depending on if it moved diagonally or not. This creates an inconsistency. To prevent the inconsistency it is best to say that it always leaves 4 squares even if 1 or 2 of those squares remains occupied after the movement.
Also @diego, the word “usually” exists in the rules for move actions provoking for a reason. Do you understand the meaning of that word? “Usually” means “not always, but often”. If something usually happens it is a first expectation that it will happen, but understood that it might not. The move action usually provokes. It does not always provoke. It usually provokes. The rules are clear that you only provoke once per round from moving through a specific creatures threatened area. It doesn’t matter if you stopped one move action and the. Started another within their threatened area or not, you only provoke once from your movement through that area for the entire round."
This statement from @chell makes the most sense to me, aside from the end of that second paragraph. I do agree there is no direct rules quote for my point of view here, but my evidence is simply in the lack of different wording in the rules.
If the rule was worded 'if any part of a creature moves out of a threatened area' i don't think we'd be having this argument as I'd be entirely incorrect that a large creature only leaves two spaces when moving laterally. But that is not the wording we have. The wording, as it stands to me, is simply a true false logic question.
-Did the creature leave the square? - Arguable
-but if asked..
-Is the creature still in the square? -True
-Then (logically) did the creature leave the square (if he's still in it)? - False
Sure, part of it moved on. But that's not the wording we have is it?
-Criteria is thus unmet for an AoO in this true false logic statement.
Does this really create inconsistency more so than if any part of the creature provokes? I dare say no - as long as 3.0 has been available this is how I've seen it ran and ran myself in turn. It works fine as long as the rule itself is consistent.
I am surprised in the amount of folks seeing this rule in another light. But with the lack of a 'direct rules quote that will ever truly answer the question' I'm afraid I'm going to have to stick to my opinion on this one, but just not for the group in question of players who singularly and unanimously oppose the ruling as I'd prefer having fun over pissing people off over a ruling that I can find no evidence for in the end.
Regardless, I do think I'm sticking to my logic statement above for the groups that have been playing in that manner since the dawn of 3.0.
There are indeed five lights here.