"I think it's dangerous from a physical standpoint," pediatrician Lisa Thornton recently told "Good Morning America." "It can lead to significant injuries to the neck and bones and ligaments."
"Mixed martial arts is coining the phrase which means, anything goes," Correia said. "They don't have any rules that are set up by any governing body."
Actually they do have a governing body, the North American Grappling Association, but so what? Hockey has a governing body, but that doesn't stop the fights, even in peewee hockey. No sport is free from injury.
In six years, 77 kids died when they were hit in the chest with a baseball. Many more died riding bikes. No one has yet gathered comparative statistics on the risk of mixed martial arts, but even cheerleading sends thousands of kids to hospitals every year.
MMA participants wear head gear and big gloves to stay protected, and the sport's governing body says it has banned the moves that are most likely to lead to injuries in children. A study from Johns Hopkins found that in MMA there are no more injuries than in boxing.
The kids at Gillett's Gym say they never worry about getting hurt. "We're not in there to hurt each other," said 8-year-old Justin Pereira. "We're all friends here. All the kids are friends and we're just in there to like, go have fun and just learn."
Justin said it helps him learn respect in all areas of his life. "It's like, you got to respect someone that's part of your family or your teacher," he said.
So do politicians really need to step in and act on behalf of parents?
"Are all parents responsible?" Correia said. "Obviously not."
So does society have a right to protect children when some parents aren't protecting them? Correia thinks so, and moved to close Gillett's without ever visiting the gym.
"I looked at the Web site," he said. "The parents do have a chance to decide that through their elected officers. That's what a democracy is all about. We run across that every day in the news, parents who are abusing their children."
But the parents "20/20" talked to don't think they're children are being abused, and neither do the kids.
"I'm his mother," Justin's mom, Connie Pereira, said. "I know what's right for him. I have no problem with him coming here. I don't care what the mayor's saying."