When you give everyone guns they will find someone to shoot. And if you listen to the NRA, then you know that just isn't true. So your statement can't be true either.
I think the issue is more the "giving" part. Because the police departments were given the military weapons, when they have a 1000 people protesting, they look at the tools on hand, a pistol, a machine gun, and a assault tank. They are then given the task of breaking up the protesters, stopping and apprehending looters, and not taught how to do that. Had they not been given the military weaponry, they would have had to gone to their accounting dept, local legislators... and said we need military weapons to handle rioters. Then the question would be asked, are military weapons the correct path, or should we buy batons and shields instead? If they needed the M-16, the accountants would likely point out, we need money for training... to go with them. When someone gives the weapons to the dept, even if they do ask accounting for riot shields, their response is more likely to be, can't you use the weapons you have? The civilian equivalent would be if I want a old bard torn down, and I offer 2 teenagers a couple AR's and box's of ammo in exchange for tearing down the shed while I leave for the weekend (and don't allow them to sell the weapons), and then hand them the weapons, it is allot more likely to be real ugly when I come back on Monday. While it is true If I instead give them $5000 to do the same job, they could go buy the AR's, but are much more likely to rent the correct tools, or buy a sledge hammer.