He does, however, take issue with experienced mixed martial artists who have lined up to call out the man who otherwise goes by the name of Phil Brooks, who has yet to have an MMA fight.
Barnett mocked Punk's would-be foes on a recent edition of The MMA Hour.
"Okay dude, you've got like 30 fights and won like three little titles in other organizations and now you want to fight the guy with zero fights?" he asked. "Ooh, look how f---- badass you are."
While the UFC's addition of Punk met with backlash in certain circles, the way Barnett sees it, there's no problem bringing him into the fold.
"I am of the ilk that does not really believe this is that much of a sport and [is] more of an event," he said.
Barnett has experience in the professional wrestling business, and in his view, MMA lies somewhere between pure sport and spectacle. As such, bringing in a new fighter with an existing fan base will help push the business along.
"At the end of the day, one has to take into account that if we don't have people's butts in the seats, you don't have people watching the events, you don't have anything." Barnett said. "This isn't the kind of thing where we've got city money and we've got tax exemptions on it, we don't have any of that kind of stuff. This isn't that kind of a business. This is far more akin to the business of professional wrestling in terms of the models of how you make money. It's somewhat similar to boxing, not entirely, but some crossover in the way they make their money.
"There's a lot of sporting aspect to what we do," Barnett continued. "But in the end, sometimes we have to go out there and give the fights people want to see, because at the end of the day, if people aren't given what they want, they're not going to tune in at all, and then none of us will have a job."
As for how Punk might fare whenever his first fight takes place, Barnett won't predict a victory or defeat. But he's confident that trainer Duke Rufous and his team in Milwaukee will have him well-prepared.
"I'm sure they're doing a great job with him up at Roufusport, and I'm sure he's training very hard," Barnett said. "I know he trained very hard to become the wrestler he is. So he's probably putting that effort right into his fight training. I really hope for the best for him."