Paabo's proven that Neanderthals were quite capable of speech and that they probably had vocabularies of 1000 to 2000 words. Further, Paabo was the person that proved that all non-African humans have 1-2.5% Neanderthal DNA.
I'm not sure how you could scientifically "prove" these assumptions. The most I believe that can honestly be said is that "It is extremely likely that ....." without actually meeting a living Neanderthal.