Indeed, "It depends".
I doubt that any reputable surgeon would agree to operate if the patient walked in and said this. The two cases that happened were widely reported in the press. One patient traveled across Europe to find a surgeon willing to do the surgery. Disreputable surgeons may be found (generally unqualified) who will take on such cases, for a fee.
Legs seem to be the body part of choice for people with xenomelia.
After the surgery, the patients declared themselves to be much happier.
They had apparently sought psychiatric help and failed to find relief there.
Was it ethical for the surgeon to operate ?
How does this compare to someone who feels like they are a person with a small nose, forced to live in the body of someone with a big nose ? Should they be given counseling and therapy to learn to value themselves and their noses. Should they be free to stroll up to any of the available clinics and pay up for a nose job ?
Society appears to be okay with the latter solution. We are then faced with someone living in an altered body, passing themselves off as someone with a small delicately formed nose when they are living a lie.