From the PHB, "A monk may thus apply her full Strength bonus on damage rolls for all her unarmed strikes" is a consequence of "There is no such thing as an off-hand attack for a monk striking unarmed".
It makes sense that you apply full Str bonus to unarmed strikes, since half Str bonus is a consequence of making an off-hand attack... of which there is no such thing for the monk striking unarmed.
Another consequence of there being no such thing as an off-hand attack for a monk striking unarmed is that he cannot avail himself of the extra off-hand attacks for fighting with two weapons or the TWF feat chain when striking unarmed, since those, by definition, require off-hand attacks... which do not exist.
I don't see how I'm quoting the PHB out of context - it says there's no such thing, and thus, full Str bonus is always applied. Both sentences fit my reading with no contradiction.
-Hyp.