What if the only evidence of an agreement was Dr. Thompson and the CEO’s handshake?

After working with counsel to modify Dr. Thompson’s lease, St. Vincent’s CEO suddenly needs a neurologist to practice at one of St. Vincent’s off-campus departments. The CEO only needs someone three days per week, and Dr. Thompson needs to pay off her medical school debt, so she agrees to fill the position. The CEO agrees to pay Dr. Thompson $37 ($39 per patient is the average in the area) for each patient she sees. The term is one year and six months and only applicable to services performed at the off-campus location. Dr. Thompson and the CEO ask counsel to write the contract, and then they both sign a written copy.

Does the agreement comply with the Stark Law?

If so, under what exception? What if the only evidence of an agreement was Dr. Thompson and the CEO’s handshake?