The black helicopters arrive and they're not going to go to the dumb beat cops and give them MIB credentials and secret alien equipment.
You are trying to make it sound silly but the federal government has been providing "local" law enforcement with military grade weaponry for years. I'm sure you know of a swat team with an APC (or two) and belt fed machine guns, and while I'm of the mind that people should be able to buy whatever it is they can afford, I'm not fond of agents of the state being armed better than citizens. I also don't like the way "local" police have started calling citizens "civilians" as if the local police were in the military or something.
Anyway, I know of no police in the surrounding towns that would turn into evil decepticons and rape and pillage and kill the local citizenry like nazi ss if the Big Giant Obama Head suddenly told us to do so on our in-car computers.
History is filled with examples counter to your point and while you may think "It could never happen here" that's what all the people were saying where it historically has happened. One way to prevent this growing problem is to make sure that the police only have those weapons they need to do their job, and to make sure citizens have legal access to those same weapons and more. Citizens are supposed to be, after all, the largest check against an out of control government.
When agents of "the state" whether "local" state or federal have significantly better arms than that of citizens, when citizens start to have their ability to lawfully purchase arms clearly infringed, when governments begin colluding to deprive citizens of arms, then it's not long before something serious is going to happen. I hope for all of our sakes that you are correct that the "local" police will be part of the solution and not part of the problem.