Sometimes, the best way to understand how another group of people perceives you is to watch portrayals in popular media. It's there where people let slip what they actually think.
As a fan of science fiction, I've been watching the new season of Doctor Who. Consequently, I've seen a couple scenes which might give a clue as to what the folks living on the islands on the other side of the Atlantic think about us.
[For those of you who don't know, the Doctor is an alien who moves through time and space fighting evil aliens and solving problems. He usually travels with two or three humans.]
The Doctor has snuck into the Oval Office and is seated in the president's seat. About 10 Secret Service agents are standing with their pistols pointed at him. The Doctor is sitting there smugly saying something to the effect of, "Really? I just snuck into the most secure room in the world and you think you are going to shoot me?" At this point, one of the Doctor's companions (who has been watching) runs into the room shouting "They're Americans!!" The Doctor jumps out of the seat and says nervously, "Don't shoot! Definitely, don't shoot!"
An American FBI agent is facing down an alien and asks it if it is armed. The alien answers back in an ominous tone, "We have manipulated you since fire and wheel. We need no weapons."
At that, the FBI agent draws his pistol and guns the alien down.
Somehow, I'm getting the impression that we might be seen as a little gun happy.