People say stuff like this a lot, mostly when they don't understand how the different forms of copyright clearances work. Essentially, it boils down to this...
1. The Cavaliers are only responsible for securing custom arranging rights. This allows them to program a show with the music licences.
2. The Cavaliers are not responsible for securing synchronization rights. That falls to the producers of the DVD.
3. Custom arranging and synchronization rights have nothing to do with each other, and different publishers may have different policies in place dealing with them, both in general, and related to specific music/composers.
4. Only arrangers/corps can apply for custom arranging rights, and only producers can apply for synchronization rights. In this case, The Cavaliers can *only* apply for synchronization rights if they plan to produce their own DVD. And even so, the ultimate answer may be wildly different for a single corps than it would be for DCI.
5. Custom arranging rights come in two flavors: Stand alone, and medley. Intent to use a piece of music in a medley can have a different cost, or even outright denial from the publisher (mash-ups are considered medleys), even when stand-alone arrangements are granted.
6. Synchronization rights are often only granted *after* the performance is complete and the recording is submitted to the publisher for approval. Obviously, this would impact DCI in a very big way.
So yea, it's not as simple as saying, "Those darned Cavies...picking a tune that wouldn't make the DVD!"