Your remark is only relevant when nit-picking corner cases involving asexual reproduction, which I don't expect to be the case in Neanderthal-Human cross-breeding.
Hence the species problem being a debate regarding generic traits, and which should count and not count, hoping to form a common definition.
Here's an example: https://doi.org/10.1016/j.jaa.2014.04.004
What's undisputed is that there are plenty of species that can and occasionally will interbreed, and yet are still considered separate species. Wolves and coyotes, for example. Horses and donkeys are famous for producing infertile offspring, but occasionally, that offspring is still fertile.
So it's not a clear-cut on/off situation. There's a gradual scale from fertility to infertility. The edges of the old definition of species can get very fuzzy. For this reason, biologists these days tend to talk more in terms of populations than species.
But this is not the case being discussed here.
With higher mammals that is not the case, and the definition of species is already well established: sexual reproduction results in fertile offspring.
Considering Paabo secured funding from the German government for a brand-new research institute in ancient human DNA and related subjects, including the right to decide what city to build the institute in and hiring authority over the initial staff, and given that he had an advance agreement with Science to publish the Neanderthal genome, I think some of these discoverers aren’t that exercised by whether they make it onto the cover of National Geographic.
Cite?
2. We can't actually test sexual reproduction of extinct "species"
3. Even if we go with the one definition of species which is "largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring", evidence of some reproduction does not speak to how often such reproduction led to fertile offspring. For example "No evidence of Neanderthal mitochondrial DNA has been found in modern humans"[1], and "Neanderthal males might not have had viable male offspring with Anatomically modern humans females"[2].
[1]: https://en.wikipedia.org/wiki/Interbreeding_between_archaic_...
[2]: https://en.wikipedia.org/wiki/Neanderthal_genetics#Interbree...
The full quote from [1]:
> No evidence of Neanderthal mitochondrial DNA has been found in modern humans. This suggests that successful Neanderthal admixture happened in pairings with Neanderthal males and modern human females.
The full quote from [2]:
> A 2016 study presented evidence that Neanderthal males might not have had viable male offspring with AMH females. This could explain why no modern man to date has been found with a Neanderthal Y chromosome.
Also from [2]:
> Positive evidence for admixture was first published in May 2010. Neanderthal-inherited genetic material is found in all non-African populations and was initially reported to comprise 1 to 4 percent of the genome. This fraction was later refined to 1.5 to 2.1 percent.
I am.
This definition kinda breaks down when we realise that wolves and coyotes can interbreed in the wild to give birth to viable offspring.
No one. That's the result of a brain fart I would edit if I could. Apologies for the confusion.
Science always brings in modern-day politics. Science, in its purest form, doesn't know of silly human foibles like “ethical restraint” or “but that's almost certainly fatal”; if scientists acted purely on scientific inquiry, the scientists who didn't kill themselves in a hair-brained scheme would either be in prison or on the run.
The classification of humans into “races” is historically associated with pseudoscientific drivel that was never particularly based on reality (much, much less so than the idea of æther); even if you've found a “race” classification that actually does have an element of truth in it, giving it the same name as the Göttingen school's scientific racism is probably not a good idea.