I assume he was taken to a US airbase and flown from there.

Americans can recall diplomats back to their home country at any time. He was recalled somewhat more hastily than most.

I imagine they said something to the effect of “you will be deported and stand trial in the US; the only question is whether you’re prosecuted in the UK as well”. I imagine that, plus promises to keep his name out of the media, were convincing.

I have to give it to the Americans their sex offenders register is public. Hopefully he or she ends up homeless and penniless.

The BBC article goes on with "He was flown back to the United States on a commercial flight, but their investigations are ongoing in conjunction with UK authorities." though.