"Remember the perspective from which the rules are written. Biped medium/small humanoid. Its simply impractical for the rules to detail out every exception for different sizes of creatures - in every place where the rules would have an interaction based on creature size. AoOs are just one place in the rules that could happen."
Yes, it'd be very impractical to go through such a list.
Yet I'm simply positing that this written rule is simply intended to be as read without adding more assumptions, and that it's not out of accident or ease of being read or ease of comprehension that the rule refers to the creature itself and not every square the creature occupies, but that it was worded as is on purpose and designed for creatures of larger sizes, not omitting them.