There's literally zero evidence shown of the extravagant claim in the title. Split skull, literally one, and no trail of evidence pointing to the killer -- f any, maybe a rock fell on his head, maybe he fell out of a tree.
As I've stated above, most carry the DNA of Neandertal individuals who lived long ago, and as we don't carry on half the possible parental DNA with each generation, the survival from just a few known Neandertal individuals mitigates in favor of the idea that they form a large part of the base of our ancestry.
dna of archaic Homo sapiens:
We are Neanderthal.
Axe heads flying off and hitting someone in the head and accidentally killing them was such a common problem that it was actually used as the example of someone committing accidental homicide.
The killer was to flee to one of the seven cities of refuge where he would be allowed to live in safety from the "avenger of blood", the relatives of the person he accidentally killed.
Having used a handled stone axe I can see how it could be a problem.