This is a pretty strong statement. I don't see why being enrolled in an institution in order to represent that institution athletically is blackmail.
High school athletics are a spinoff of the academics, not the other way around, nor are they are separate entities, which is why there are academic requirements to compete. What academic requirements does a home schooler need to meet to compete?
Does your thinking apply to college athletics too? Can I try out for the University of Texas football team (a University partially subsidized by my tax dollars) if I'm not enrolled in the school? How about if I just pay tuition but study elsewhere?
What part of *The parents are living in the district and paying school and property taxes* escapes you?