IO540, that's exactly where the difference between a flying school and a flying club comes in.
At my flying club, the club is run by pilots for pilots. Yes, we have instructors, but all of them are freelance and any agreements between the student and the instructor is between them. The club does not get involved and actually, after a flying lesson, you have two bills to pay (separately): the aircraft and the instructor. Although the club does facilitate the instructors by publishing the "standard" rate for an hour of instruction, and offering members the ability to book an instructor together with the plane, on the internet reservations system.
Obviously instructors are club members too, and since they hang around the clubhouse a lot, they actually have a lot of informal influence. But formally, instructors are equal to students to PPL holders as far as the club rules go.
Club activities are activities where everybody is invited. Student, instructor, PPL holder. Bring your own plane if you want, or take a club plane. In fact, some of our club members have bought their own plane and rent it out to club members via the clubs reservation system - although you have to be checked out on these aircraft by the owner first.
We even have people who did their PPL with the club, then went on towards ATPL and have 737 jobs at our airport. They are still very welcome for activities or just to hang around the clubhouse.
So it is very well possible to have a separation of club activities and commercial activities within one organization. But I have found that it does require a board, composed of volunteers, that actually recognise this fact and do their best to maintain that separation in a logical way, that still works for everybody.