It’s equally possible that there was more than one or even a day where only people were born and no one died.
There was a low point where only about 2,000 humans were estimated to be alive. Certainly you couldn’t have had someone dying everyday then
I read the full paper and I’m not qualified to evaluate the validity of the model being proposed but I find the idea that the population was
rather implausible. Implausible things sometimes turn out to be true but models frequently turn out to be wrong so if I were to bet, I would bet on the latter.
Plus, for the purpose of the OP, I think neanderthals and other close relatives of modern humans should count as people even if they have no living descendants.