My understanding is that you can charge a fee but it’s technically under your supervisor’s license, so they may have to set it, I think. For example, a colleague did postdoc hours with a private practitioner; her fee was $150 (her supervisor set it) and she had to disclose her status on a page of his website (and as part of consent). Her supervisor provided the office and kept $75/session to balance out the time he spent supervising, administrative, etc.
This was a few years back now, but was perfectly ethical per the BOP.
Edit: the regulatory language dictates that the psych assistant is an employee, so the supervisor has to employ them and pay them a set wage (in my example, $75/session was the wage, which varied by caseload). This is how you get around the fee issue—“employees” paid per service, with the supervisor charging the fee paid to the psych assistant and providing a wage).
I’d check with the board for further clarification.