One difference between (a) and (b) is that (a) is a competitive league (NCAA) with its rules on eligibility -- "amateur" (however this is defined and if enforceable), age limit (generally must enroll within one year of high school class graduation), five years to play for four years, etc. To the extent that these rules are enforceable, the school has to abide by them.
For representing the school in its band, the school can make the eligibility call.
For representing the school in its band, the school can make the eligibility call.