You're right that the distinction between violence and fatal violence is significant, but we have zero reliable evidence on the incidence of non-fatal violence perpetrated by the two sides.
The quote you provide is meaningless. In the first place, it is merely anecdotal. For every anecdote demonstrating the initiation of violence by police, we can find other anecdotes demonstrating the initiation of violence by protesters.
More importantly, police are required by society to use force. Society has laws; sometimes people break the laws. The people who break laws may not honor a friendly request to come down to jail to be arrested; we must hire people who will force them to enter the justice system. Sometimes this absolutely requires the use of violence. The problem is NOT that police use violence; the problem is the determination of the appropriateness of the violence they apply.
In the case of Mr. Floyd, the use of violence was flagrantly and egregiously unjustifiable. But in many of these cases, the use of violence is much more problematic.
For example, in the case of the NYPD SUV that drove into a crowd, the video demonstrates that a police SUV was under attack. People were pelting it with stuff. Now, from the video, it's clear that the stuff being thrown is not a serious threat. But if you were inside that police car, hearing things hitting the car and seeing people all around you, and being blocked from moving forward, you would most likely have panicked. How were the police inside the car to know that there was not a fellow preparing a molotov cocktail with which to set the car on fire and roast them alive?
That's the critical point that you are ignoring: the police must respond to PLAUSIBLE threats, not just PROVEN threats. Many of the people surrounding that police car were being violent. They are the ones who initiated the violence.
In Buffalo, where two police officers were severely disciplined for pushing a fellow, the entire riot control section resigned. 57 police officers flatly refused to participate in riot control under conditions that they believed were impossible. We've been excoriating the police as an institution for the last 10 days, and many police officers have been disciplined for improper acts. Whether they are right or wrong is a matter of judgement. We can condemn them, but if the police decide that the demands we place upon them are unreasonable, then police will refuse to do their jobs.
There are always two sides to every story.