To be fair, in the vast majority of cases, this is exactly what happens... cop engages brain, realizes that the situation either either something dumb, mistaken, or impossible to prosecute (and is otherwise not a crime), says as much to the complainant, and moves on. Or, in the case of what may be a crime but turns out to not be, same-same, with maybe a stern talking-to of the 'offender' that maybe he should not be so dumb in the future, or at least don't make the activity appear so damned suspicious. ...and then there's the small minority of police officers who are either overeager newbies, had a really bad day, decides he doesn't like the guy, didn't get laid the night before, a closet sociopath, or suchlike.
About the same sample size as humanity at large, really, but with one subtle-yet-important distinction: force.
But yeah, otherwise, a blanket statement like yours is, well, a blanket statement that holds little meaning in the real world, since most police already do use their brains before acting.