You're right, the "liberal at 18" quote has never been actually verified, so he very likely never said it, but Churchill was obviously in the Conservative Party.
I don't get your point though. It doesn't have anything to do with the American politcal sense of liberal and conservative, which is why people dig up that quote. In the quote you provided, he's using liberal in the broader scale, where Reagan and Clinton were both liberals (the broader sense being that you believe in liberty and freedom as a right for all people, as opposed to social liberalism), not the micro-sense where Reagan was a conservative and Clinton is a liberal.
Sean Hannity uses the quote he's arguing for social conservatism and against social liberalism, and the quote you provided doesn't exclude the possibility that Churchill said it, because he could have been talking about a different sense of liberalism.