Funding would most likely come from the FCO or DFID budgets, so quit stressing about where the cash is coming from. The fact the international aid budget was the most probable source of funding should please the daily mail readers on here - the RAF gets a lot of coverage (rightly so) for doing a bally good job, plus it gets spent on our assets.
As for the Whys and the Wherefores, consider this, if said nurse was to hide their symptoms and come home on the next BA jet direct to heathrow, as I think many would do in the circumstances bearing in mind the sort of treatment you can expect in Sierra Leone, I ask you to bear a thought about the carnage that would be wrought for the 200+ passengers sharing the trip (most probably on the Abuja leg).
The offering of aeromed services (funded externally to MoD core) has more to do with containment as it does with
PR.