I've actually had dealings twice with American policemen whilst on holiday there, the first when I was pulled over for 'swerving' on an motorway and the second for speeding.
In the UK once you are on a motor way you basically drive in a straight line and any traffic joining it 'merges' into it from an entrance filter lane adjoining it for a third of a mile or so. Seems in America that's not the case and the joining traffic stays in their 'lane' and the existing motorway traffics lane dog legs accordingly to accommodate it. I not knowing this was simply holding my lane when all of a sudden vehicles suddenly 'cut' into it causing me to swerve to avoid it.
It just so happens there was a police car behind me who pulled me over. Once he could see I was a tourist who had made a simple and unknowing mistake he became very helpful and even give directions and guided me part way to our destination, Niagara Falls.
The second for speeding was me rushing along a road (a three carriage motorway type road) to get to the next town (tens of miles away) to find a motel for the night, as it was late and dark with no one about. I think the speed limit was 60mph but I was doing 70 (which is the speed limit over here) and maybe pushing 80 on the down hill sections. I'm not making excuses, I was in the wrong but there was only my vehicle on the road, I never passed anyone, the road was that empty and I don't even recall seeing much if any traffic traveling in the opposite direction. Anyway out of nowhere I could see a car in the distance and could see it was gaining on me so guessed that it might be a policeman - and it was.
Again after finding out I was a tourist and clearly just looking to find a motel for the night for me and the family, was friendly and helpful and didn't give me a ticket.
I guess like everything there are good and bad people in every job and maybe I was traveling in areas where the colour of your skin was not such a big issue and crime wasn't a big problem and so the policemen I met weren't on edge or something and more relaxed in dealing with me? I was also fully compliant and respectful to both officers also and totally accepted I was in the wrong both times - don't know if that also helped in how they dealt with me also, maybe it did with some of the examples you have given above about how others are frightened of being stopped by the police?
Obviously in the twenty-first century the colour of your skin should not be an issue and until we are able to get to that point then I guess we can't claim to be yet civilised.
Hopefully though that day will come soon, here's hoping anyway.