That's a heavy accusation that I clearly needed to look into.
It turns out that the statement is accurate. Specifically, SEC Bylaw 220.127.116.11d, section 8, states:
In order for the visiting team marching band to perform at half-time, the visiting team must request
permission from the host institution’s Athletics Director by February 1. If the host institution’s Athletics Director does not grant permission, the visiting team marching band may not perform at half-time. (Effective for competitions after August 1, 2014.)
This is cause for concern, or at least it could be, if athletic directors choose to use it liberally. I'll admit that there are times that such a rule makes sense. For example, if a Homecoming game will feature, say, the crowning of royalty or recognition of a Hall of Fame team, there may simply not be time to include that as well as both bands' halftime shows. Consider that the one game Ohio State's band is not traveling to this season is the Northwestern game, because it fell on the Wildcats' homecoming and they would not have had the opportunity to perform at halftime. What's unclear is if this new policy simply adds formality where there was none or if it changes the previous policy.
Where it gets sticky is what the Pride of the Southland fears. They state that an athletic director could choose to fill the space with marketing or canned music, and they certainly could. What's just as bad, this could be used for gamesmanship, rivalry fuel, or simply spite. Auburn could choose to deny the Million Dollar Band a chance to perform simply to stick it to their archrival. An athletic director could attempt to minimize a rival band's presence to gain a competitive advantage or maximize their own home field advantage. While denying a band a spot at halftime doesn't keep a school from bringing their whole band, it greatly disincentivizes it. And simply a pep band, especially in a packed, loud, SEC stadium, almost isn't worth the trouble.
The SEC has a great tradition of band travel. Even with incomplete data, the conference well eclipses all others for Band on the Road games. It would be a shame to see this go by the wayside, especially since, as a standard bearer for college football, what the SEC does could easily influence other conferences. On the other hand, this could be a non-issue. Similar to the way all athletic directors agreed to grant teams' requests for white jerseys at home, I would love to see common sense prevail for the good of the sport and the preservation of a true college football atmosphere.