I was under the impression that the PJI's who wear the two winged badge on the right arm do so because they have passed the relevant physical test ie either P Coy, Pre-Para or All Arms Commando.
This should also apply for the TCW / TSW / MAOTs. No physical course pass should mean the light bulb. Of course the majority haven't passed it and walt around pretending to be an airborne warrior....
I know of only 1 RAF Regt member who has not passed any of the 3 above courses who has his wings, but then again he'd got to the end of selection.