I'm resurrecting this just because I want to be clear about not only the rules say (in Tennessee, in that school district, and elsewhere), but what people think is ethical and right.
I'm a private coach who also coaches XC and track at the school where I teach. None of my running clients are (or ever have been) students at the school where I teach and coach. I think of that as the bright line -- my kids at the school are my kids at the school, and they deserve the best I can give them because they're my students and my student-athletes.
I'll say this: early on it was hard to figure out how to balance the time commitments, and initially there was a definite pull toward the private clients when time needed to be prioritized. (This would be mostly at home, making training plans, going over practices and old performances, communicating with athletes, etc.) The urge is to meet the needs of the paying customer first. But then, I decided that my student-athletes are paying, too -- my salary as a teacher and my stipend as a school coach. Maybe not as much. But eventually I had to make a decision for my own sanity as to who would get first priority for my time, and I decided it had to be my school team and those kids. I suppose it's because most of the kids at my school could never afford a private coach and thus were reliant on me, alone, to do the best job I could for them. There are enough private coaches out there that a kid (and parents) who can afford one can go and find someone else if they need to. I lost a few clients, but I'm up front about it now: my school gets first priority, and I'll do the best I can for paying clients after that. I have a good rapport with some of my private athletes, and that arrangement is fine with them; some parents want to pay for your sole attention, and I've had to part ways with them amicably. I also charge less than I did.
I want to say that, and this might seem defensive, but there are good reasons why being a private coach is the best fit for some coaches. First off, paid coaching positions at high schools and colleges are tough to come by, even if you just need a little stipend to pay for your time and travel. High school coaches in lots of sports, track/XC among them, really enjoy what they do, for good reason! It's fun and rewarding and is a constant (interesting) challenge. Anyway, you could be a very qualified track/XC coach and not be able to find a paid coaching job. Even volunteer jobs are not _that_ easy to come by -- HS and college XC/track coaches don't need an infinite number of volunteer coaches on the staff.
Private coaches, if they keep their numbers limited, can give the kind of individual attention to an athlete they can't get from their high school coaches, especially if their high schools have large teams and their coaches are good about spreading the love around the team and trying to develop everyone, and not just focusing on the stars.
Years ago I was an assistant coach at a high school that had a girl who was an all-American and heavily recruited. She had been coached since she was 10 by the same club coach, who was a totally legit sprint genius. She came to all our team's practices, and even was one of the captains of the team, but she always had her own set of workouts from her coach, with whom I talked every once in awhile. I figured I didn't know half what he knew about sprinting, that I could learn something from overseeing her workouts and even stealing a little bit for my other sprinters, and so I would just oversee her workouts and make sure she was healthy and resting properly, and it worked out great for everyone. It seems like that might have been something that might have worked at Brentwood, without the private coach having to actually join the coaching staff, which was the step that raises all the ethical questions.
A question arose early in this thread about whether it was ethical for Coach Avery to "solicit" clients from Brentwood HS. Certainly not, I think that's clear. But I also think he might not have had to do any solicitation himself. Once you develop a reputation as a coach in the area, all you really need is the word of mouth of parents and athletes. Still, I think it's smart to keep a firewall between whatever your side hustle is, and what you're doing for kids at school.
I don't actually expect anyone to respond to this, I think I just needed to think aloud.