The "typical US police encounter" really isn't what you see on Liveleak or WSHH. In the vast, overwhelming part of the US, it's more like my experiences:
My shooting club in MA (when I lived down there) had the only dedicated "class III" (full-auto) ranges in the state and we had a standing and open invitation to any local/state/fed law enforcement that they could train there. They weren't allowed to "take over" the range, but could work in with the civilians. So that is how I ended up helping out with the FBI guys one morning when they came with their MP5s. They were good, but weren't (IMHO) balancing right with the SMG on their front foot and were riding it up. So we worked on that.
At the end, we had some fun blasting bottles and cans.
THAT is what most real Americans experience with law enforcement.