i have never been stopped by police, and on my business i go to places a lot more dangerous than Peru ::) Its common sense and be alert.
Yes usually this safe thing is bring out from Americans, do not know the psychological impact in that. Like the question is that area is safe? happenned a zillion times and the source of the question is always the same.

Happy travels everyone ::)
ps and I was at the May 1 celebration in Paris, lots of police with guns and riot police behind the scenes in trucks, nothing happenned but it could be scary if from a country not used to these celebrations. It was great walks with two visiting friends from Florida USA!