Was the human race given an ever-lasting boost by breeding with Neanderthal man?

So many articles make the point about the evolution of the human race after we left Africa.
Read about it here.

Experts believe that modern man and Neanderthals shared a common ancestor in Africa.
Around 400,000 years ago, early Neanderthals left Africa and headed for Europe and Asia.

However, our ancestors stayed behind and evolved into modern humans.

Professor Parham’s results could be explained by interbreeding between the two ‘tribes’ passing immunity to disease developed by the Neanderthals after they’d left Africa our way.

The professor told a meeting of the Royal Society in London that this interbreeding instilled modern man with a ‘hybrid vigour’ that allowed it to go on and populate the world.
‘Rather than having to evolve from scratch as they moved out of Africa and into Europe and Asia, this interaction would have provided a fast-track to adapting to new environments.’

See here and here and
here.

Neanderthals are amongst our ancestors but not the ancestors of present day Africans.