Wait is that a requirement?
The answer is no, however doctors who are wintering at Australian Antarctic stations are required to have their appendix removed. This is because there is usually only one doctor on station during winter, and evacuation back to medical care in Australia is impossible for at least part of the year. The requirement dates from the 1950s, when an Australian Antarctic doctor developed appendicitis on Heard Island and required a very challenging evacuation back to Australia.
In 1961 a Russian doctor successfully removed his own appendix at Novolazarevskaya station in Antarctica. With no outside help possible, he used local anaesthetic and had two expeditioners assist with surgical retractors and a mirror so that he could see what he was doing. The operation was a success and the doctor was back on duty within two weeks. It's not a situation that Australian Antarctic doctors would like to find themselves in!
As part of their overall medical review, all expeditioners are required to have a dental check before they depart for Antarctica within six months of their departure date. There is no requirement for expeditioners to have their wisdom teeth removed unless the dentist identifies that they may cause a problem over winter. The station doctor has eight days of training in emergency dentistry as part of their preparation, but this does not include wisdom teeth extraction.
http://www.antarctica.gov.au/about-antarctica/people-in-anta...
No helicopter in the world has such a range, so the only means of evacuating is by ship, with the fastest ships in the area taking minimum 3 days to make the trip. If a navy ship is around, it could probably treat the emergency on board but most others will have to get back to Réunion first.
In the likely event that no ship from the French navy is around, the fastest means of evacuating will be requisitioning a nearby fishing ship but those will probably not make it to Réunion until at least one week.
Fortunately, the relative emergencies (but not life threatening) I have witnessed have always happened when a ship was already on its way for other reasons, but US or not there are real technical impossibilities in these places.
Edit: it seems that aetial refueling for helicopters is a thing as well.
Aerial refueling though I guess could work, although I suspect that no suitable tanker airplane is to be found within range anyway most of the time (and no suitable helicopter either) as the military base on Réunion is not a major air force base and there is no other country than France with decent forces in the area. Australia has tankers but they're on the wrong side of their country, nowhere near Perth.
I think we're getting beyond very, very expensive here and into the territory of things no country would do outside of extraordinary circumstances, the kind of circumstances in which the country operating the base would not matter anyway as most others would cooperate in any way they could.
The Americans, of course, would just attempt surgery on site using remote assistance from stateside surgeons, do the horrendously expensive evacuation when it goes wrong, try to bill the patient for the entire multi-million dollar amount, and then base a screenplay or teleplay on the story.
Apologies for the source, but I remember reading the same thing in a better source too.