drnuncheon said:
Page 125 says: "You can use a double weapon to make an extra attack as if you were fighting with two weapons." So, obviously, you only get your 1/2 your strength bonus to the other end of the weapon (since that's how 2WF works.)
(It is not "obvious" at all that you get 1/2 your Str bonus to one end when using a 2-handed double weapon for 2WF. But it was clarified a long time ago, and it's not an issue now.)
The quote you posted is irrelevant here. When wielding two weapons (and thus using the full attack action) you get certain penalties to your attacks, and a reduced Str bonus. An AoO is a single melee attack at your normal attack bonus. A single melee attack is not two-weapon fighting.
Kreynolds made up a rule saying "when you attack with two weapons, you suffer the two-weapon penalties until your next action." This is what you should quote from the PH to substantiate.
Now. Where in the PHB do you see the option to switch from two-weapon fighting to one-weapon fighting in a single round? Answer: you don't.

Why do I need that "option" spelled out. Each round you get one turn and on that turn you can perform one or more actions. Once an action is over, any further actions or AoOs are based on your new situation unless the rules say otherwise.
If you do a double move, you get further AoOs based on your situation at the end of the move. Even if you couldn't make an attack action during your turn and spent most of it in a different location.
You're fighting for the entire round as if you were using two weapons - just like Power Attack or Expertise lasts for the whole round.
Both power attack and expertise
specifically say that they last until your next action. The rules don't say that about the penalties for two-weapon fighting.
Otherwise you'd get jokers that say "OK, I'm going to attack as if my double sword was one weapon...now I'll switch and use it as a double weapon to attack with the other end...now I'll switch back to using it as a single weapon for the rest of my attacks."
If you want to fight with two weapons (or both ends of a double weapon) you have to do it with the rules for two-weapon fighting. That's in the rules.
What's not in the rules is that you are assumed to be fighting with two weapons after you are, eh, not fighting with two weapons anymore.
Since D&D combat is an abstraction, this is the only thing that makes sense - it's not like batle chess, where your piece comes alive, whales on the opposition, and then freezes while other people take their turns. You're not hitting the guy 5 times in 1 second and then standing around picking your nose - you're making that AoO in the middle of your 6-second attack sequence.
AoOs do not depend on what "makes sense". Any AoO(s) is(are) made at your normal attack bonus even if some, logically, would have come after an attack made at a different bonus, or at a time when you were in a different location.