The problem with American values is that they have no perception of longevity. They cannot view problems over the horizon of what they are staring at.
Talking a bit from my experience - I am still someone with a Serbian heritage. I can asure you, that this is not the problem really. Or definitely not the biggest one. People understand the american definition of freedom very well. What worries them is what's left of it when it arrives here - with here I mean in general the kind of actions that take place in nations like Kosovo or Syria or Lybia, Irak etc. I believe that the higher ranking officials in the US government and military know very well what they are doing.
I think the CIA had some report somewhere which shows that the war on terror and counter terrorism by the US governement since 9/11 actually increased the attacks, terrorism and hostility against US citizens. Drone strikes for example are one of the top arguments by terrorist groups for recruting members. And some of them have never seen as much popularity like today. On the other side the US military has increased their budged to vast proportions since the late 1990s, particulary after 9/11 though.
The real thing is, with (islamic) terrorism the US military and government can create a win win situation. On one side it creates a constant situation of fear while not beeing actually realistic threat - the chance to die to a terrorist attack for the average US citizen is what? 0,1%? And it is also not likely that religous fanatic muslims will overthrow the US government any time soon. But it makes it easier to concentrate on foreign affairs rather than domestic policy and pacing questionable/uncomfortable laws and it allows the military to increase their budged every year. A Win-Win situation.