Would it be legal for someone to Thunderbolts his Avengers team and choose Fantastic Four, then play the Fantastic Four card to change the team ability? At first I thought it was ok but then thinking about it I thought I had read somewhere that it couldnt be done.

You cant you have to have FF team in the first place to use it

You probably read this (from the Marvel E&C):

Characters assigned the Thunderbolts feat may not choose a team ability that is granted by a feat card when choosing a team ability.

So if you choose "Fantastic Four" when you T-bolt, you'll get the original Fantastic Four TA. No ATAs allowed.

That's where it was. Thanks!