There are a number of "tests" used to determine whether someone is self-employed; these include: control of what work you do and when you do it, how the work is done, who corrects errors, whether you provide your own equipment (aircraft, headset, charts, instructional gizzmos), who pays for maintenance of ratings and medicals, who finds a replacement if you are unable to work (illness, etc), and several others. By careful use of these "tests" it should be possible for people who genuinely are self-employed to prove it.
Maybe one (slightly devious?) scheme would be for a school to provide a loan to the instructor so that they could part-own an aircraft and therefore provide some of their own equipment - that would need some careful preparation.
Bogbeagle
I'm always surprised at the "us and them" attitude that some people perpetuate - in most industries this dissappeared decades ago and, if there are areas of the flying training industry where it still exists, it needs to be beaten to death. We all need to help with this. Organisations always work better when people work as a team and understand each others viewpoints - this benefits everyone.
BTW, I agree with your point about charging.
HFD