Modern humans and neanderthals apparently did not interbreed. I went into the issue thinking that there probably was some relationship, judging by the body type of certain regions, but the evidence is pretty conclusive. Neanderthals left Africa half a million years before modern humans, and when Cro Magnons got to Europe, they did not interbreed. Whether they interacted, we don't know, and maybe never will, but my bet is that there were territorial battles that our kind won, and which led to Neanderthals' ultimate demise.
If two animals can breed then they are the same species. If they say Neanderthal and man interbreed then they are saying Neanderthals WERE men.