There are essentially four “Concierge” models:

Fees for care. In this model the fees charged are directly related to medical care, as described by the IRS, and would generally be considered as eligible medical expenses under the HSA guidelines.
Annual Physical. Here a fee is charged for an annual physical, usually comprehensive in scope, that includes no [...]

Is an otherwise eligible individual who has access to free health care or health care at charges below fair market value from a clinic on their employer’s premises eligible to contribute to an HSA?
An individual is not prohibited from contributing to an HSA merely because the individual has access to free health care or health [...]