When you get in the cab, the cab driver is going to have some sort of conversation with you, I'm guessing... where you want to be dropped off and the like. If you say anything that makes him think you're expecting a free ride, he'll pull over and let you out (example: "Thanks for helping me out, I really appreciate the kindness of strangers", "Thank goodness you're giving me a ride. I'm broke and can't stick around this po-dunk town another day!", etc).
So no, he is not "liable" for his assumption that you're paying. The sign on the outside of the cab states the fares. The cab driver doesn't have to restate them to get money from you. LOL