Actually, a licensed medical doctor can legally do a ton of things that are not "FDA approved", including perscribe medications for off-label use (for treating something it is not designed or approved to treat), and perform elective surgical procedures or implant devices that are not FDA approved. This is all legal and actually done quite often. However, if there is a problem later on and a medical review board determines that the doctor acted negligently and put the patient in danger, that can be cause for loss of license... but simply implanting a non-medical, non-FDA approved device does not mean they are risking their license. Just practicing medicine is a risk.. that's why they call it "practicing".. no joke.
The other big issue with non-FDA approved uses for medications or implanting non-FDA approved devices, is that many medical liability insurance companies will not cover the doctor in these instances... it's the same if you make renovations to your house without a proper permit and inspection, or do electrical work that is not permitted and inspected.. if there is an issue later, your homeowners insurance will not cover you in that case... so with doctors they are perfectly within their legal and ethical/moral right to implant our products, they are simply taking a risk that something could come back to bite them later if you wanted to be an asshole about it... so, just remember that when talking to any professional (piercer, doctor, or vet), they are risking their livelihood on your one-off request.. show the proper respect and maybe they will take that risk on you.