Seems to me the parents and the girl want it both ways. They want the benefits of school extracurricular activities gained by going to public school without going to school there.
This girl doesn't go to school there. Her parents (and maybe even the girl) have chosen for her not to attend school there. They therefore disqualify the girl from participating in activities that enrolled kids get.
If she wants to be in a school band, enroll in school there. You can't and shouldn't be able to have it both ways. They need to make up their minds what they want.
This sounds a lot like what liberals would whine about.
Therefore, if we were to stick with your logic, public schooled kids shouldn't be able to play music with any other band (or sports team, or whatever) besides the one public school supplies...even if their parents pay for it with their tax money, correct? This is, in essence, what you are telling the homeschooling family.
You are way off base. Obviously the girl's parents want her to have a better education than what she can get in the public school. They pay taxes and the school should allow her a spot in the band IF she makes the competitive cut.
It blows my mind that people like you begrudge someone who wants a better education the ability to join in on some extra-cirricular activities. Otherwise, its taxation without representation. As long as the kid is good enoug to make the team/band/, Big brother shouldn't be allowed to take your money and slam the door in your kid's face.
Also, a school band or team represents the community - not just the school itself. For example, the Yankees and Padres represent the states that they are from, not just their parent corporations...