If I'm reading the trait correctly, it looks like it works similarly to Perplex, in that when you use it on a character, it stay in effect for the entire round, regardless of where the affected character ends up at by the end of the round. Correct?

DEPROGRAMMING: Give Doc Samson a power action and choose another friendly character within 4 squares and line of fire. That character can't be affected by Outwit or Perplex until your next turn.

You are correct.

Thats how it looks from where I'm sitting.

OK, here's a hypothetical situation:

My Wolverine is based with an opposing character that he has just attacked (and failed to hit). On my opponent's turn. He attacks Wolverine, and then Outwits Wolverine's B/C/F.

On my turn, if I move Doc up within 4 squares and L.O.F. to Wolverine and use the Deprogramming ability on him, Wolverine now gets his B/C/F back immediately, right?

this is correct.