I think the term "Christian" is so ambiguous that really anybody can claim to be a Christian and it will mean something completely different from another person of another religion claiming to be a Christian.
Also, it is a little like claiming to be the one and only "true" religion. Many religions make this claim, and they all look at each other and say "No, you're not. We are." They do the same with the claim of the being Christian. They all look at each other and say, "We're the REAL Christians!"
Personally, I think they're all full of shit.