We might be thinking of different generalizations here.

Almost certainly. I am specifically referring to the generalisation quoted by David. It is, in fact, exactly the reasoning I used when I donated to the SIAI. Specifically, I estimate the probability of me or even humanity surviving for the long term if we don't pull off FAI to be vanishingly small (like that of winning the lottery by mistake without buying a ticket) so donated to support FAI research even though I think it to be, well, "impossible".

More straightforward examples crop up all the time when playing games. Just last week I bid open misere when I had a 10% chance of winning - the alternatives of either passing or making a 9 call were guaranteed losses of the 500 game.