It's fascinating that Neanderthals were apparently able to cook. However I'm not sure it has a great deal of relevance to the diet eaten by paleolithic humans, who were a separate branch of the evolutionary tree.
Nevertheless they may have picked cooking up from humans, who had been cooking for many thousands of years before. The human paleo diet was pretty broad, with a lot of vegetables, fruit as well as animals, particularly the guts and brains.
What is interesting is the evidence of cooked starch grains from barley. Were humans also eating this? They may well have, which would broaden out the human paleo diet even more.
It was considered that humans out-survived neanderthals due to their broader diet, but that may have to be rethought.
Mark