The point about cops and criminals having almost identical psych profiles is almost an exact hit on the head. Its of said that serial killers are the best profilers (whose job it is to catch the monsters in the first place). The biggest problem is that in order to catch some of the really bad criminals out there, you have to be able to think like them
This is why you see the dichotomy in cops. I've known ones that are the typical thugs in uniform, and I've seen others who are the kindest people in the world who are genuinely concerned about the people who they protect.
Fortunately never been in a situation where I've mouthed off to a cop, but I have been in ones that I was most definitely at fault. I was apologetic, agreed with everything he said, and actually walked away with a much smaller fine than what I deserved.
That said, the right to an attorney is there for a reason. A lot of the shows that are on TV now seem to be pushing the idea that "no one lawyers up unless their guilty". I think thats a load of something unmentionable. The cops have ways of getting you to say what they want you to say. The first words out of anyones mouth when they get to the precinct (after keeping their mouth shut until then) is "I want a lawyer." Period.