I think I've figured out why the monk +TWF is so screwed up: it's a mistake WotC made from the 3.0 to 3.5 conversion.
If you remember, a 20th level monk in 3.0 had an odd iterative attack progression: +15/+12/+9/+6/+3.
The familiar flavor text is in a slightly different order, but very similar. For instance the second paragraph reads:
3.0 PHB said:
A monk's attacks may be with either fist interchangeably or even from elbows, knees and feet. There is no such thing as an off-hand attack for a monk striking unarmed.
And what's the very next sentence read?
3.0 PHB said:
A monk fighting with a one-handed weapon can make an unarmed strike as an off-hand attack, but she suffers the standard penalties for two-weapon fighting (see [...]). Likewise, a monk with a weapon (other than a special monk weapon [1]) in her off hand gets an extra attack with that weapon but suffers the usual penalties for two-weapon fighting and can't strike [2] with a flurry of blows (see [...]).
First off, note that the old monk's attack bonus closely resembles the new monk's flurry-of-blows, and that the old monk's flurry of blows was nothing more than exactly TWF but then only for monk-special weapons. Without the old flurry, a monk using TWF and a weapon is very very similar to the new monk with TWF and flurry, and similarly, a new monk with TWF (for unarmed attacks) and flurry is very similar to an old monk simply with flurry.
I think what happened is that they botched the conversion. The old special unarmed attack progression went the way of the dodo, and in those reforms, the specific two-weapon fighting text got lost. But note: the 3.0 monk explicitly said
both that
"There is no such thing as an off-hand attack for a monk striking unarmed" and "A monk [...] can make an unarmed strike as an off-hand attack, but she suffers the standard penalties for TWF"
The old situation was clear: the monk could make up to five unarmed attacks, and use off-hand weapons with TWF (and by extension, ITWF and GTWF) for up to 8 attacks per round. The new situation simply fails to precisely specify what is and what is not possible, but I think it is clear that the sentence "There is no such thing as an off-hand attack for a monk striking unarmed" was copy-pasted to the new revision from the old, where it definitely wasn't meant literally. I don't think it is meant literally in 3.5 either.
If that's so, then I think the FAQ's interpretation is the most balanced one, for although it does add rules (which should properly be in an errata), I think the rules added are consistent and within the spirit of the written rules, and finally fill a gap in the PHB - i.e. they don't contradict it.