No disagreement there, just pointing that interbreeding is a natural default hypotheses given that we know that at some point their living areas began to overla

No disagreement there, just pointing that interbreeding is a natural default hypotheses given that we know that at some point their living areas began to overlap and the Neanderthals eventually disappeared as a distinct species by that taxonomy - the debates afaik are about the scale of the phenomena that is whether they were mostly absorbed by modern humans or mostly driven to extinction or even killed by them.