Do Americans censor "real" violence more than theatrical violence? Possibly. Do they censor "real" violence less than any form of nudity? Yes.
You can show Braveheart or a video of a street mugging to a bunch of 8-10 year old kids at school but you can't show them a movie where (god forbid) a pair of tits appears on screen. At the very least, the uproar will be an order of magnitude larger for the boobs as compared to the violence.
And once again, this is not the norm around the world. The US is special.