This is the story as understood by Sturtivant: it does not seem to reflect the real situation in the Middle East.
I have found Bruce's notes, and are available here;
http://www.clubhyper.com/reference/wildcatfaaba_1.htm
They include a correlation between the Bu Nos and the British serials, for the majority of the aircraft.
3872 was indeed one of 16 such aircraft on temporary loan: this was a typing error for 3875 which I will now correct.