Population geneticist Montgomery Slatkin, graduate student Fernando Racimo and post-doctoral student Flora Jay were part of an international team of anthropologists and geneticists who generated a high-quality sequence of the Neanderthal genome and compared it with the genomes of modern humans and a recently recognized group of early humans called Denisovans.It is not clear to me when you make the species break but for two species to interbreed several hundred thousand years after they split is unusual. Dogs and wolves, for example, don't have nearly that time depth. The split must have been a very subtle one, then. As to how they know that Neandertals interbred without having two related Neandertals on hand, here is the explanation:
The comparison shows that Neanderthals and Denisovans are very closely related, and that their common ancestor split off from the ancestors of modern humans about 400,000 years ago. Neanderthals and Denisovans split about 300,000 years ago.
In another analysis, Jay discovered that the Neanderthal woman whose toe bone provided the DNA was highly inbred. The woman's genome indicates that she was the daughter of a very closely related mother and father who either were half-siblings who shared the same mother, an uncle and niece or aunt and nephew, a grandparent and grandchild, or double first-cousins (the offspring of two siblings who married siblings).Depending on how large the population was, this may have been a necessity. it may also be an artifact of sampling. This happens in modern human populations as well but is not common. As the authors note, there are quite a few unanswered questions. For example, they really have no idea how much interbreeding between Neandertals, Denisovans and modern humans took place.