I doubt you get charged in a mutaul combat situation. Self defense during a fistfight is a very easy case to beat
Hmmm...most of my info is not 1st or direct 2nd hand, but every time it's come up IRL, or on the web, in non-mutual combat situations it seems like unless there are witnesses if you win and do damage, if someone goes to jail, it's going to be you. Because the damaged guy is automatically the victim, or so most of the stories go.
Have never had to deal with cops in a fight/scuffle situation, personally. My dad did once, but there were no witnesses, not much damage (my Dad lost) and it was "He said, she said." LOL kidding about "she." That was a lot of years ago, though, and in a place where cops regard their job as genuinely to serve the public, because they get paid well there.
The boxing family was in a different state -- not sure if it was a mutual combat state, but most fights aren't mutual combat (i.e. one person usually initiates and the other, without consenting, either fights back or doesn't). Worth noting: even in mutual combat states, you can still go to jail for disturbing the peace, etc. (in which case, the state is considered the victim).