I'm having a major disagreement with my local group regarding the Outsiders TA. I had a situation where my opponent used it on one of my figures, and on my turn, I wanted to Perplex up its defense. My argument was that, even if I can't modify it while Outsiders is in effect, I can still target my figure and the modifier would apply on their next turn, unless they target my figure again with Outsiders. They argued that, because I can't modify, I can't make the target at all. They didn't cite PROTECTED at all (commonly PROTECTED: Outwit), but I feel like that's what they're translating into this. Of course, the difference is that PROTECTED explicitly prevents the targeting of such a thing and ends any such effect. I admit I'm scarecrowing a little bit with that PROTECTED argument, but I'm trying to understand their argument.

Your friend is wrong. You are correct. Nothing in Outsiders prevents being targeted by Perplex.

Their argument is entirely incorrect.