I can't see the difference between a "stranger off the street" and a friend - after all, aren't strangers only friends we haven't yet met?
Legally though, I don't think there is any difference. If your club has its own rules that's different but if I was in that situation (and I have been), I'd take the person up.
I Self-Fly Hire from a school and they have never asked who (or what!) my passengers are or what the financial arrangements are.
As far as I was aware, the PPL who is prepared to cost-share is not permitted to advertise but if someone wanted to cost-share, then I can't see why they can't put up a card.
Cheers
Whirls