Rebirth vs Reincarnation

For years and years now I've been an atheist, going to church for family events just so my mother doesn't get upset, and mumbling out prayers to beings that I don't think exist.  Then I started reading about Buddhism, and realized that I already believe in many of its core ideas, so I read up more.  I liked what I read about the causes of suffering, how to avoid suffering, and how the medical community has conclusive studies proving meditation is pretty goddamn awesome.  Then I got to the part about "Rebirth"...

I don't believe in life after death or in purgatory-like states.  I believe that Buddhism is a way to improve yourself in this, your only life.  However Buddha preached about many planes of existence where your mind may spend time after you die, where gods and demons abound, and that after intense meditation he could recall his previous lives.  This is really the only disagreement I have with the Buddhist canon.

I've talked to a friend of mine who's a history major and he tells me that I cannot claim to be Buddhist without believing in everything they say, and I fired back by asking him if his views coincide exactly with what the Vatican tells him is right, which shut him up, but I still wonder, can I claim to be Buddhist without believing everything taught?

My current view is this:  The people who preach this have had experiences similar to those before them, and that is why they teach this.  If so many people preach this, there has to be some link, whether or not intense meditation or desire caused hallucinations, there is still a link.  I can follow the rest of the teachings, and if I have an experience that lends credence to the other things, I can believe that too, if not, then I know it was because Siddhartha was raised in a religion that taught those things, and they arose in his subconscious while meditating.

Logically does my current stance hold?  Can I call myself a Buddhist or not?