That's the kind of logic used to justify lynchings. We have a legal system that enforces a certain burden of proof, that takes place in a courtroom where strict procedure is enforced by an ostensibly impartial judge, and evidence is weighed by an impartial jury. The system is carefully set up to balance the rights of the accused against the interests of the community. It may not work all the time, but it exists for a very good reason, and mob justice is no substitute.

I know on paper that is how it's supposed to happen but if we are honest it doesn't always happen that way.

When the legal system is perverted by local corruption and nepotism, allowing bad actors to run roughshod over their victims, are they supposed to just lie down and take it out of dedication to an abstract principle which has been wholly betrayed in practice?

I mean, they should not just lie down, but I think the more lawful and orderly approach would be to appeal to a higher tier of authority that's supposed to be available within the legal system. Of course, easier said than done, but still I think that's what the "right thing" would have been.

The Constitution provides for an impartial jury, along with other important factors. A lynch mob is no such thing.

How many of the mob were directly impacted by the bully?

I could imagine having witnessed the bully be a bully, not being a victim, and still deciding the bully needs to die. The decision can be made not based on the desire to defend yourself, and instead based on the desire to defend others / the desire to prevent unjust behavior.

This was a mob execution.

A jury that is inconsistent and hard to rouse. The subsequent crimes show the criminals their understanding of the broken justice system