I don't think this is particularly unique to cops. When you're trapped and cornered, you desperately resort to any possible approach to get out of it. Acting incredulous or indignant when you know you've messed up, with the small hope it will get you out of it, is a very common human thing.

> with the small hope it will get you out of it

That's the thing, with how much cops will put on the kids gloves if it's an officer I'm certain the hope isn't small that they'll get out of it. The videos you see of cops getting arrested they are almost always completely blasted.