But he showed his ID, which proved he wasn't the right person, and at least two of the deputies already knew him personally.
Even after confirming he wasn't the suspect, they still detained him, used force, and later discussed whether they could justify an arrest anyway.
You're confusing the timeline.
1: they stopped him. Said they had a warrant, asked for his name.
2: He gave his name, the same name on the warrant.
3: arguing.
4: Warrant check. Says the name he gave.
5: Detainment. The force may have been a bit much, but considering the temper he'd shown, it was I think within acceptable range. They didn't slam him or break anything. They put hands on and detained him.
6: Talked to him, here is where he's fully recognized by one of the other deputies. Name remains on the warrant.
7: They ask and find out he is not the guy from the warrant, it's another guy, a relative, with the same name.
8: discussion