I think they could have made it Agent Nobody of SHIELD with a sniper rifle and the scene would have been exactly the same. The only reason to make it Hawkeye is to tease his character for the Avengers movie, but if his character is just "some guy in SHIELD" that isn't anything worth crowing about.

I'm the first to admit Hawkeye's backstory won't work in one of these movies, and short of devoting half of an Iron Man sequel to him there isn't room to do him justice. But it's lazy to just cram him into SHIELD and it detracts from what makes him special--he's the carny who decided he could hang with iron men and thunder gods with nothing but arrows and stubborn pride.