Case in point: When I'm wearing my 1st Recon Beret, I have the required Perception to take the "Better Criticals" Perk, but without it I am one point shy. Will wearing my Beret allow me to select that perk?

No, it won't, you need to have the required stat at that level 'naturally' for perk purposes. This applies to skill boosts as well, you cannot use a magazine to boost a skill 10 or 20 points in order to reach a level of, say, 70 from 50 or 60 in order to qualify for a perk.

Well I guess I can scrap my current character, then. Ah well. Good to know now as opposed to level 16. Many thanks!

If you haven't already gotten the perception implant, that will count towards perk requirements.

Yeah, I was counting on the perception implant AND the Beret. Thanks for the heads up, though.

Could you squeeze in an Intensive Training?