This simply can't be true. How could such a change happen and spread to all populations on all continents at that point in time? And I'm doubtful about the first claim being scientific fact, too.
The
human brain has been shrinking, beyond that which can be explained by average changing body size, for thousands of years, across most of the human population.
Many genetic changes have accelerated over the past 10k years- some of seem to be related to neurology. (this has been linked to what's called domestication syndrome) That
cognitive modernity enabled humans to spread in Europe- about 40k years ago- was long-accepted in archeology.
No, it's not great evidence for saying that modern humans are cognitively superior, with there existed plenty of archeological evidence against this; it's also the absolute bottom of the range, and you can't really prove that there wasn't that there wasn't a cognitive shift 10k years ago (or 40k years ago)- which is the point; the evidence is sparse.
To be clear, my estimate for cognitive modernity tends toward the higher end of the range; IIRC we found evidence of
H erectus using complex multi-step tools equal to qhat we ascribed to Neanderthals until we discovered them using birch-bark glue.