I want to thank Kazaan for some of the most polite and thoughtful discussion I have read in a while. It's easy to get defensive, circle the wagons, and refuse to acknowledge the value of an opposing line of thinking, but he's consistently made his case while acknowledging the value of the alternate interpretation.
Reading this thread has convinced me of one thing for sure, which is that the archetype as written is ambiguous.
If Kazaan's preferred interpretation (#1) above is the one intended, then the word "only" would have been a really helpful addition by the author. It's only one additional word, so it wouldn't violate the spirit of economy and brevity Kazaan argues for.
On the other hand I agree with Kazaan that the fact that they do NOT use the word "gain" is also significant, which is a point in his favor. As is the general spirit of the archetype.
Interestingly, the flavor passage "The unarmed fighter picks up a weapon only rarely, and when he does, he prefers the weapons of the monk" seems to me to cut both ways. On the one hand it leans obviously in an RAI sense towards Kazaan. But then again, if the UAF is nonproficent in all non-monk martial weapons, the flavor passage seems hardly worth mentioning -- of course ANY character is going to prefer weapons he is proficient in over weapons he's not. But it would be worth mentioning if the intent was: He received enough training at 1st level to be proficient in all martial weapons, as any fighter would be, but as he progresses as an UAF he becomes more likely to prefer fists or a monk weapon, since he gets more and more bonuses with these.
Anyway, I think Kazaan summarizes the two options well. The text needs only a tiny word added to clarify which is intended.