The PHB doesn't say anything of the sort... with the exception of it being one of the results after a successful grappling attack.
After re-reading the section, I have found the bit that I thought stated an unarmed attack made the attacker move into the opponents square:
PHB p140:
Attacks of Opportunity: Attacking unarmed provokes an attack of opportunity from the character you attack, provided she is armed. The attack of opportunity comes before your attack. An unarmed
attack does not provoke attacks of opportunity from other foes, as shooting a bow does, nor does it provoke an attack of opportunity from an unarmed foe. You provoke the attack of opportunity because you have to bring your body close to your opponent.
Now, I will admit that it does not state that an unarmed attacker moves into an opponents square. However, it does imply that you have to move the position of your body (bring your body close) in order to make the attack. Because of this, I don't believe that an AoO can be made, because a person making an AoO is not allowed to move as part of the attack (rather, an AoO takes place when someone moves in close to you). However, an AoO could be made from someone moving into the square you occupy, as you would then not have to move to make the attack.
The rules do seem ambiguous, but considering all information, I believe that unarmed characters do not threaten an aread. The main convincing point to me is the Sage's statements.