Longtime boxing promoter Lou DiBella took part in the "boxing vs. MMA" debate with Joe Rogan on ESPN a couple of years ago that you see above, but he said in a recent interview that he doesn't think the growth of the UFC's popularity has had anything to do with the decline of boxing's popularity.
From DiBella's interview with John James of The Sweet Science:
LD: MMA does not hurt boxing. MMA does not destroy boxing. Boxing fans aren't running to MMA. That's just all b.s. The reality was that long before MMA and the Fertittas [brothers] spent a gazillion dollars with the UFC, boxing was already fading. Boxing's biggest problem is that it can't attract young people. We have virtually no fans under 30, and that's a problem. ...I agree with DiBella that boxing fans aren't running to MMA, but boxing definitely needs to learn some lessons from the way the UFC has marketed its fights. I question whether anyone involved in boxing will learn those lessons.
JJ: Is boxing losing popularity to MMA ?
LD: No, it's not losing to them. They are gaining popularity on their own and we are not gaining popularity.