Getting a 'compassionate' passenger to destination a.s.a.p. is one of those events in the AT/AAR world when everyone pulls together knowing that even a couple of minutes could make the difference between the passenger seeing their loved one alive or deceased.
I've no idea of the circumstances of this event, but if the TriStar arrived to make a normal landing only to find that the flaps, for example, wouldn't extend, then it might well be necessary to reduce weight to enable a flapless landing to be made. Putting the gear down would help to burn off a little quicker whilst checking the figures for a flapless landing, so that the fuel dump time needed would ultimately be shorter.
Routinely if it was necessary to dump down to flapless landing weight, one would find a suitable area to avoid disturbing the locals. But if that meant a longer delay for the compassionate patient, then I'd say to hell with it and dump at the minimum acceptable height to expedite matters... RAF crews aren't slaves to the QRH, unlike some airline people-tube drivers and are taught to make pragmatic judgments.
Anyway, being Jockistanis they were all probably out with buckets trying to catch the Avtur...
