The link doesn't work. If this is the link that he said he'd run on the Democratic ticket, DUH. Do you know how party endorsements work in NY? You'd be a fool not to have as many as you can, especially in a 5-1 D city, where independents also lean D.
It's worthy of note, that in 1983, Ed Koch had the backing of both the Democratic party and the Republican party in NYC. It didn't make him a Republican any more then this makes Giuliani a Democrat.
To your larger point, a person's past actions do have something to do with their future actions, but it's not the only indicator. If I had judged Ronald Reagan's future by his past, I'd expect that he'd liberalize abortion laws, raise taxes, and generally be a center-right or even Nixon like Republican. Oops. Guess that didn't work out so well.
Reagan was a democrat and later admited he changed his views on abortion. I can't speak for Nixon because I don't remember where he stood on that issue. Rudy admits he supports abortions still, so there is a difference between the two.
You know NY politics better than I do. What you said about party endorsements is similar to what someone said over on the youtube thread. Another poster answered by saying this: