That's true, may be a slightly confusing way to interpret it, given that C = A∪B. In context I think it's better to read it as P(A|B), in the case that C occurs.
That's true from an objective, mathematical standpoint. But the paradox is really saying something about how humans perceive the statement, so different (mathematically equivalent) ways of framing the same thing can make a difference. It's a minor point.
or even more precedence dubious: P(A|B|C) ?