Medical expenses that are eligible for FSA, MSA, and cafeteria plans are determined by the government.
Below are the IRS documents that list and explain what is eligible.
IRS document 213(d) https://www.usu.edu/hr/files/uploads/213(d)eligiblemedicalexpenses.pdf
Makes it very clear that payments to physicians are an allowed deductible insurance.
Then if you look at IRS document 502, http://www.irs.gov/pub/irs-pdf/p502.pdf
Medical expenses are the costs of diagnosis, cure, mitigation, treatment, or prevention of disease, and the costs for treatments affecting any part or function of the body. These expenses include payments for legal medical services rendered by physicians, surgeons, dentists, and other medical practitioners. They include the costs of equipment, supplies, and diagnostic devices needed for these purposes.