The issue was whether the formulation makes sense, not whether it makes frequentialists freak out (and it's not substantially different than e. g. drawing from an urn for the first time). In either case P() was the probablitity of an event, not a hypothesis.

In these sorts of problems you are supposed to assume that the dollar amounts match your actual utilities (as you observe your exploit doesn't work anyway for tests with a probability of <0.5*10^-9 if rounding to cents, and you could just assume that you already have gained all knowledge you could gain through such test, or that Omega possesses exactly the same knowledge as you except for human psychology, or whatever).