Again, you've restated the argument so that it at least makes sense logically. Whether that's what the original report intended to say, but for some reason just couldn't bring itself to say, is a matter of conjecture.
I suspect the confusion is deliberate, and possibly related to your additional argument that:
allmendream post 35: "Neanderthals are distinctly non human."
Let me suggest:
if we sort of "accidentally" confuse the very tiny subcategory of "unique genetic markers" -- of which apparently 1% to 4% are identical between Neanderthals & Euro-Asians but not Africans -- with the entire human genome of 3 billion nuclear DNA "base pairs" -- of which 99.5% are identical amongst humans and Neanderthals -- then we can with apparent reasonableness argue that "Neanderthals are distinctly non human."
In truth, the DNA evidence -- even leaving aside possible interbreeding -- suggests that Neanderthals are distinctly human -- 99.5%.
That 1% to 4% apparently refers only to the last one-half of one percent -- the same percentage by which humans differ from each other, and also from Neanderthals.
So let me put this as simply as possible: if humans can differ amongst ourselves by one-half of one percent and still all be "human," then why cannot Neanderthals differ from us by one-half of one percent and also still be "human"?
How is their one-half of one percent less "human" than ours?
Do you not agree? ;-)
Even the most distantly related human populations shared a common ancestor within the last 100,000 years; neanderthals diverged as a separate unique population some 500,000 years ago.
In morphology they are distinctly neanderthal, not human.
In DNA they are distinctly unique, and show the evidence that the fossil record supports; that they diverged some five times longer ago than even the most distantly related human populations.
You assumptions of extrapolation of the 1-4% ancestry as being a 1-4% difference and that being the same amount of difference between humans and neanderthals is flawed.
The 1-4% ancestry is based upon markers and does not denote a 1-4% genetic difference between humans and neanderthals. Neither is the genetic or genomic difference between human populations and between human and neanderthals the same amount of difference, but five times less.
In other words, if you found a DNA sequence where two human populations differed by 0.1%, you can expect to see the neanderthal sequence differ by around 0.5%.
In the chart of genetic distance between human populations that I posted, the farthest branching would only be around 20% of the distance between the branching of humans with neanderthals.
Given the diversity of human characteristics (short dark African Pygmy; blond blue-eyed Scandinavian; Japanese; etc) it makes more sense to consider Neanderthals a different race of humans rather than a different species, given evidence of interbreeding.