I call myself a pilot, more importantly, so do various licencing authorities. I have flown 49 types as pilot in command, which is somewhat above average (96 types in total, I've often not been PiC, particularly in a flight test environment - but that most certainly DOES NOT give me an excuse not to know the aeroplane).
Fairly regularly I have to go and fly something I've not flown before. Depending upon how novel it is to me, I might *only* spend half a day looking through the manuals, preparing kneeboard cards, and if I possibly can fly with an experienced pilot on type for an hour or more.
If I'm flying something as PiC that I've not flown before (it happens occasionally) I'll normally allow myself a couple of days preparation with manuals, speaking to anybody who knows something worthwhile about the aircraft, preparing abbreviated notes to take into the aircraft with me. Then when I fly it, I effectively check myself out in the air - with a few gentle hops, careful handling investigation in the middle of the envelope, and as I build up my knowledge of the aircraft, get towards steep turns, Vne, stalls, and so-on. I'll normally try out a few missed approaches and flap selection/retraction practices at a safe height too.
Interestingly, the older (and presumably more experienced) I get the more I feel the need to do all this preparation. At the same time, I seem to find aeroplanes frightening me a lot less when I'm in them. I wonder if these two are related?
That said, I think that most pilots (frankly I don't think that it matters whether they're a PPL, ATPL or military) could self convert to an aircraft in a familiar class. BUT, have they been taught how to do so? - in most cases I suspect not. It is, incidentally one of the more important things they teach trainee Test Pilots.
G