The neanderthal was too far from us for us to be descended from him and Heidelbergensis was further. DNA tests would show that; it seemingly hasn’t occurred to anybody that dna tests on Heidelbergensis materials would be possible.
“The neanderthal was too far from us for us to be descended from him and Heidelbergensis was further.”
—I think you’re misunderstanding what is meant when scientists say that Neandertals are not our ancestors. They don’t mean that in the sense that Neandertals did not give rise to Homo sapiens - that part is already clear since the Neandertal species is no older than our species. What they mean is that if one had a family tree going back 30, 40, 50 thousands years ago, you won’t find any great granparents where one is a Neandertal and the other a Cro-Magnon.
So what it currently looks like from the dna evidence, is that when the Homo sapien and Neandertal lineages split (presumably from Homo heidelbergensis), the two lineages stayed split and didn’t interbreed. Thus the dna evidence currently backs those that argue that Neandertals should be categorized as a separate species, or at least a subspecies.