Everything that you say is correct; however, it's a risky proposition for the Republican party to focus on it, because it papers over the dire straits in which the party finds itself.
I'm not American, so this is an outsider's perspective. I think that the Republican party does focus on the truth that Bush won the election over Gore and that he won it fare-and-square. In doing that, they ignore the more salient truth: since 1992, the Republican party has won the popular vote for president exactly once.
That is a sign of a party out-of-step with the country they want to govern.