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People who work in some profession often have thing called "professional deformation". For police it is specifically valid: when everything in your life is filled by pretty specific kind of people, you start to expect everyone be like them, and often begin acting like them (because there is no other way). It requires serious amount of will to prevent yourself from becoming thug when every person you interact is a thug who rarely understands anything except force. Especially considering that people who go to police already aren't big humanitarians either.
American police has specific local problem: they work in environment full of armed people who don't care about prison sentences and may shoot on sight just for fun, especially in some ghetto regions. So they already have deformed enough personality that forces then to shoot first and think later. It saves them in most cases, but when case is different they just can't act in other way.
I think any amount of training would be useless for US police until they'll fix their complex system problem with crime-ridden regions, but there is no reasonable solution in sight.
> no doubt Hungarian police could have dealt with the situation
I guess that if you fill Hungary with large amount of weapons and people who don't afraid to use them everyday, your police also would transformed to something like this in few years.