Here how I read it: Unarmed Combatant is a class feature that allow to use your unarmed strike as a monk unarmed strike. In other words, it doesn't give you proficiency into monk unarmed strike, it transform your unarmed strike into a monk unarmed strike.
I see it just like the Rogue class feature Rogue Weapon Talent, that allow you to use a dagger at +1 att or shuriken at one damage die greater than usual. So these class features takes mundane weapon usable by anyone (unarmed, dagger, shuriken) in a more deadlier weapon (monk unarmed, dagger +1 to hit, shuriken at 1d6 damage).
And the only way I see to allow another class to have access to such thing, it is by creating a multi-class feat. Every is proficient in unarmed strike, but not everyone have the psionic training to turn there unarmed strike into a monk unarmed strike.
Once you have access to that class feature, all feat that apply to unarmed weapon applies to monk unarmed strike.