Wow, you folks are awesome! Thanks for all of the input on the subject. It seems that most people agree with my player, you do not take the -2 penalty when making only one attack. I will begrudgingly concede the point and let my player make a regular attack roll.
However, please let me make one final attempt to make my case and then I will drop the subject :-)
I will start with my basic assumption of the six second round where you make your attack. I don't envision the character as standing still, like a lump, for 5 seconds and then taking a 1 second swing.
To me, combat is abstracted and during your turn, your character is clashing swords with the enemy, dancing around, feinting, dodging, looking for an opening to make a good strike. The one attack roll represents that one opportunity per round.
Maybe my assumption is wrong, but I envision all those movie sword fights you see. Following my assumption, the TWF character is using that other weapon to block, parry, etc. during his six seconds. He is actively employing two weapons to fight his opponent.
Dictionary.com defines wield as:
"to use (a weapon, instrument, etc.) effectively; handle or employ actively."
To me, the key word in that definition is actively. It is part of the fighting style. It is not an optional on/off toggle, like say Power Attack.
The TWF feat states "You can fight with a weapon wielded in each of your hands."
Also, take a look at the Two-Weapon Defense feat. It states "When wielding a double weapon or two weapons (not including natural weapons or unarmed strikes), you gain a +1 shield bonus to your AC."
Seems to me that you get the +1 bonus to AC whether you make one attack in a round or multiple attacks. Why? Because you are actively employing, or wielding, the TWF style during the battle.
Now, if this was a home game, I would just make a ruling and be done with it. However, we are playing Pathfinder Society and I want to play by the "official" rules. It would be great to get an official ruling. Thanks for reading this far ;-)