Most classifications have Neanderthals and modern humans as separate species and the DNA evidence does show hybridization.

The definition of species is actually a human construction to define organisms. Nature is often not as "accurate".

For what it is worth, the Mule Deer (Rocky Mountain, California, Desert) are actually the result of Whitetails (bucks, I think) mating with Blacktail does. Which makes it truly interesting for the geneticist/classifier that the two "true" species in the mix are the WT and BT with the Mule being the hybrid offspring who have now become a full species and somehow absorbed, for classification purposes, the original species as a sunbspecies.