Are Neanderthals the same species as us?

Chris Stringer at the website of the British Natural History Museum:

The biological species concept states that species are reproductively isolated entities – that is, they breed within themselves but not with other species. Thus all living Homo sapiens have the potential to breed with each other, but could not successfully interbreed with gorillas or chimpanzees, our closest living relatives.

On this basis, ‘species’ that interbreed with each other cannot actually be distinct species.

Critics who disagree that H. neanderthalensis and H. sapiens are two separate species can now cite supporting evidence from recent genetic research. This indicates that the two interbred with each other when they met outside Africa about 55,000 years ago. As a result, everyone today whose ancestors lived outside Africa at that time has inherited a small but significant amount of Neanderthal DNA, which makes up about 2% of their genomes.

In the face of this seemingly decisive evidence, why do I cling to my belief that Neanderthals and Homo sapiens are distinct species?

More here.