Let's see. Can an opponent outwit my battle fury then mind control me?

it a yes, as long as the power says posses, and they cant if the power says "this power can`t be counter", is a trait, or for a external source that says "this character can use"

It is not listed as unoutwittable, so yes!

Cool, thanks! It seemed strange, though maybe because it never came up before.

Probably because everyone looks at (or used to look at) Battle Fury as a negative power for the character possessing it. As time (and the rules) has progressed, it has only become more of a beneficial power. Case in point: it prevents you from being Mind Controlled or Incapacitated. Saved my Worldbreaker's butt in the past.

You want to Incap an indomitable Battle Fury character? You have to have lots of extra outwits!

I have had multiple occasions where someone says "okay, close combat mind control on Hellboy/Atrocitus/whoever" and I say "nay, nay!"

I outwitted it once on an opposing character so I could mind control it so he could attack a character in stealth. My opponent was so annoyed (and confused him at first). This was back when it only stopped you from making ranged attacks, couldn't be carried and stopped you from being mind controlled.