I remember having discussions about this in my master's program. As I recall, there was at least one instance where a program was forced to drop the private lessons requirement because the parents did take legal action. It's basically pay to play even if you're not the one pocketing the money.

The parents having the ability to pay for lessons is irrelevant.

From what you've described, the student is clearly good enough to be in the varsity band. This leads me to believe that it's not about this individual student. You're afraid of what happens if you let a student who's not in private lessons into the varsity band. If other students/families see private lessons as optional instead of mandatory, will participation in lessons drop? Or have you built a culture where everyone buys into the idea that lessons give you the skills necessary to be in varsity and it's only the rare exception that can get there on their own?

I understand that fear. I understand the broad perspective and thinking about how this affects the program as a whole. However, from a narrower perspective, it really is unfair to this kid who clearly deserves to be in the top band but isn't allowed to unless their parents spend more money.

The parents are absolutely justified in their perspective that their student is being treated unfairly. Actually taking legal action would be cost prohibitive, but if they do have money and are willing to fight on principle, they could.

My question is, if you don't want this fight, what really happens if you let this kid in? Is anyone else really going to know? Is the kid going to go around bragging about how they made it in without being in private lessons? Or, if asked, can they simply say they take lessons from someone outside of school like they claim?

My $0.02