And to give an example of something somewhat similiar: I once accidentally took the wrong bus on Erev Yomtov. Instead of ending up in Yerushalayim, I ended up in some random city that I’d never even heard of. The only way I had to get to Yerushalayim at that point was by taking a taxi.
I made a calculation and figured out that if the taxi speeded the whole way there and back, it was theoretically possible that he could make it back before shkiya. I asked someone who said that I was allowed to do so.
I think there was a very good chance that the taxi driver was mechalel Shabbos since he had no reason to speed back home (unless he was Shomer Shabbos which is possible, but it was more likely that he wasn’t), and I’m not even 100% sure he could have made it back with speeding. I was not comfortable with this and would not have done it if not for the fact that I really could not imagine spending YomTov in a random not-Frum city where I did not know anyone. And I was told it was okay. And the possibility existed that he was not mechalel Shabbos.
I have always felt bad about it, but I really couldn’t imagine doing things any different.