The Pdoc would be the one to decide that. Most medical doctors (Pdoc) require insurance, don't have anything like "sliding fee". But insurance with a Pdoc works differently than insurance with your T because they are a medical doctor.

Insurance is almost always the cheaper route. It is harder in the first few months of the year because of high deductibles but that still comes out cheaper than if you had to pay $125-150 a session for PDoc if you did not have insurance. Probably the lowest he would go is, say $80/$90 and that's probably the same as the insurance rate you pay until your deductible kicks in.

Insurance IS a sliding fee scale; they get a "discount" because you are part of a group that has lots of people and if they did not accept that, all those people would go somewhere else so they would not get that money. People without insurance have to pay the regular rate and anything privately negotiated with the doctor/mental health person is probably going to be close to the insurance rate they get paid. Some therapists do have slots for one or two people they give sliding fees to who have no insurance and cannot afford to pay, etc. but that is an individual decision by the health care worker, usually a T, not a doctor/Pdoc.