Gasp! Deadpool would NEVER do that.
 
And on the ID's... I'm totally missing the boat here. Wouldn't Tony and the government (or at least the government) know Cap's real name? 

 The guy who's DD had a house, so, fine, fake ID - I'll buy it. But for Cap, and even... well, I dunno, some of the others, do they really go "home" to somewhere other than their Super Secret Underground Command Base (TM)?
 
Meh. It depresses me that the boat's left and I'm not on it. Maybe I'm putting too much absurd thought into this.