but most of the rioters were there that day because they believed in some conspiracy theory

Or at least that was their esxcuse to wreak havoc and show their disrespect for any kind of common rule that should not be broken.

If you go there saying you're protecting your president from Hillary Clinton's gang who rallied in a pizza restaurant owned by HC herself but it was actually a cover up for a pedo-ring of satanists who also drank blood, well, even if you don't believe it when you say it, don't be surprised if they'll frame you as cop killers.

Psyops go both ways: sometimes you punch, sometimes you get punched in the face.

So no, that's not reason for distrust of the government, that's reason for not taking reports too seriously and read between the lines looking for the actual information, buried in the noise.

The reason for government distrust in USA is fabricated by those powerful people that do not want to make it obvious that they are abusing the rules and use the common people as human shields to protect their shady interests