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Your story about the clueless frozen pair crossing your path is a scenario I've sometimes thought about but has never happened yet: I'm not sure what I'd do if it looked really serious.
Unfortunately it's something I've had happen to me on more than one occasion. I had a chap come up to me on Burbage moor asking if I'd seen a sheep fold? It turned out he was using a guide book sketch map to navigate with. I said "This Darbyshire there are thousands of sheep folds here about's." (Actually I think it's South Yorkshire but you get my drift). I sent him back to Hathersage.
I was with a party of climber one very wet Saturday in Llanberis pass, for something to do we decided to race up the Parson's nose route and back via the north ridge of Crib Goch. This was some years ago when I was a bit fitter and fell running was a thing. Once we'd got up onto the ridge we found a party of about twelve medical students in quite a panic. They thought they were on the Pyg track. Three were hyperthermic, one was nearly unconscious. Fortunately there were enough of us so someone shot off to call out the rescue team, this was pre mobiles. Two people stayed with the casualties and two more shepherded the rest down to Pen Y Pass. The two with the casualties ended up staying with them all night.
It's also happened a couple of other times but then I was going that way anyway so just said "come with me."