He’s been convicted of beating his current wife/girlfriend or whatever they are and his phone conversation he had that was recorded he says he punches his kid to teach him respect. So no it’s not false.
Fiction can be fun.
When the entire tape was released there was a previously unreleased part of the conversation where Hill and his son's mother discuss how he didn't do anything to deserve being arrested and that she sold him down a river.
He also never punched his kid and after a very extensive investigation was found to have done nothing wrong.
I assume that being in the KC area we have been exposed to more of the actual truth of this situation than the rest of the country.
The current NFL doesn't let people play if they think there is a chance of a player being guilty of the type of accusations you are throwing around. Not a conviction, just a chance. He has been thoroughly investigated by both law enforcement and the NFL and there is nothing there.