I agree- unarmed strikes are a subset of unarmed attacks.
Monks are highly skilled in fighting unarmed, giving them considerable advantages when doing so...A monk''s Attacks may be with either fist interchangeably or even from elbows, knees and feet. This means that a monk may even make unarmed strikes with her hands full, There is no such thing as an off-hand attack for a monk striking unarmed...
And:
1) The only weapons usable with Flurry of Blows are monk weapons.
2) Unarmed attacks are weapons (according to the equipment section & chart).
3) A monk's unarmed strike is a subset of unarmed attacks, and thus, a weapon.
4) A monk's unarmed strike is usable with Flurry of Blows.
5) Thus a monk's unarmed strike is technically a monk weapon.
6) Thus you can use a grapple with the FoB, according to the FAQ.
For your position to hold water, you'd have to argue that a monk can fight with his unarmed fighting skills one way and its an unarmed strike (with a monk weapon), and another way and its merely an unarmed attack (without a monk weapon)...
Or that they only unarmed strike while FoB?
That he's consciously using an attack form that is suboptimal, so he can't use all of his training?
Is grapple an unarmed attack? Certainly; it will benefit from Ki Strike and bypass DR X/Lawful. Can it be performed as part of a Flurry of Blows? No; it is neither an attack with an unarmed strike, nor an attack with a special monk weapon.
As I've shown above, the monk's unarmed attacks
are a special monk weapon.
He could flurry and grab with his hands, or even initiate a leg lock.