Nope. The only background checks I've ever had working for Americans was law enforcement / intelligence agency software (I was working for a Canadian company and they sold to them) and a contract for the Nasdaq.
Other than that, it's just been straight skills and reputation. Even if it did come up he could always say that he assumed they would ask for a background check if they cared about this type of thing. Just let the man get some work and move on with his life.
I believe you, but I haven't. Though I haven't done much large sized tech company work other than the Nasdaq gig I mentioned, which was background checked.
I think the overall point doesn't really change. Apply. Let other people dismiss.
I think it might be fair to point out that just because they ran a BGC on you, doesn't mean your current employer told you they did. Background checks are incredibly common and the low-stakes kind are pretty cheap to just run ad-hoc.
Other than that, it's just been straight skills and reputation. Even if it did come up he could always say that he assumed they would ask for a background check if they cared about this type of thing. Just let the man get some work and move on with his life.