I think what it is saying is that it influenced both ways. Neanderthals shared immunities against certain diseases with Modern Humans, And Modern Humans shared Immunities against other diseases with Neanderthals. Those who ended up surviving the exchange because they had the best of both immunities combined as hybrids are now us.
Thanks O, but if that's what the article were saying, it wouldn't have "Neanderthal extinction" in the headline and "modern humans were able to wipe out Neanderthals in Europe and Asia" in the article body.