Once more, if the doctors own the airplane and employ you to fly it, you're acting as a corporate pilot. If the doctors don't carry other passengers or cargo to a point other than the point of departure for revenue or compensation, and exercise operational control of the aircraft, and you merely fly them at their request, you can take them where ever they want to go as a commercial pilot.
NBAA, airlines, FSDO...all irrelevant and only serve to cloud the issue and the question. You don't need the permission of the FSDO to act under your commercial pilot certificate. The doctors don't need the permission of the FSDO to own an airplane. The FSDO doesn't have the authority to grand or deny those privileges, except in issuance of your original certificate, or enforcement action against the same.
Again, perhaps a more important issue is weather you should undertake this task when the attorney for your future employer (the doctors) tells you it can't be done. When the attorney for doctors tells me something, regardless of weather it's right or wrong, I have to consider the weight of the money and the capability to act. A little like a pedestrian insisting on the right of way over a semi truck. Not necessarily a wise idea...until their own attorney is in your corner, proceeding against his counsel might be the most foolish thing you could possibly do aside from making love to a porcupine.