I've traveled throughout the US inner cities for the past few years with a Contax P45 (now +) and 1Ds2. yes I have insurance, but no, I don't want any trouble.
I look scruffy always. once when I was sitting on the kerbside in a run down area, someone stopped their car and tried to give me money as a homeless individual. the camera under my jacket was worth more than their car, but it was hard to explain that. kind people abound. The other tack is to put on an orange hi visibility vest, then everyone assumes you are from the city or some utility co. works well.
only time I got physically in trouble was when I took a picture of an unoccupied car, from afar, in a parking lot in LA suburb. the owner turned up and went ape, god knows why. tried to throttle me with the camera strap, till I deleted the picture. people are weird.
my Contax has the name taped over, of course, and I use a bag that doesn't look like a camera bag. amazes me that Tamrac, Loewe etc make bags that scream PRO PHOTOGRAPHER at the world, when its not what we want 90% of the time.
the best camera I had for this kind of work was a Plaubel Makina, it folded up to a small paperback book, despite being 6x7 MF, and you could put it over your shoulder, then put your jacket on, walk down the street and nobody had a clue you had anything. swing it out from under your arm, pop the lens forward, take a picture, and back again. just great.
I hate these big, unwieldy mf DSLR's, but there's not a lot of choice in digital these days.
Alpa 12TC maybe, its kind of got a homemade look, and if they sold an accurate rangefinder, I'd probably switch.