What happens to Captain America?

Nope. Godfather makes it pretty clear by bringing up Frick that he basically takes a hands off approach to officers (or as he puts it "supports them" no matter what is said). He is pointing out that there are folks who also object to Frick -- but what is he suppose to do that if he acted on all the griping he'd be screwed.

He states that Capt America was within the box and given the conflicting stories he heard he would do nothing.

Basically he doesn't give a **** as long as the job gets done, he gets his glory and there's not clear proof. At most he is implying that he might keep an eye on Capt America, but I don't think he'd even go that far.