Problem is that I do not see any way that the people who say this can actually know that about the animals in question that they refer to. To look at modern apes, well, Man has some 6,000 cultures at present to judge purely by languages (itself a dubious means to do so IMHO) and these cultures range from monotheistic monogamous post-industrial civilizations with military-industrial complexes to agrarian polytheistic polyandrous civilizations rooted in a mutation of Hindu culture to the various shattered remnants of Indigenous peoples of entire continents in the shadow of the former civilizations.
In the quadrumanal apes there's the orangutans, who are solitary apes, there's the gorillas who are organized in harem societies (it's good to be the silverback in gorilla society), the common chimpanzee, which exists in patrilineal societies that engaged in repeated conflicts between group for their brothers' land and wimmins (sound familiar) and Bonobos who people are starting to realize are Not So Different from their other cousins in the wild.
The problem for me with this is that people try to read the behavior of 21st Century human societies in that of both human ancestors and human ancestors in that of modern apes. The Neanderthals and australopiths did not necessarily behave like modern apes. To read behavior of completely different animals in the light of each other in that manner is somewhat foolish because in today's world we have primarily one bipedal species and four quadrumanal ones that occasionally walk on two legs. In the past bipedal apes were rather more common, and given that orangutans and chimpanzees in certain areas can differ drastically enough that the term culture could be applied to both, why exactly is it that we do not attribute this to human ancestors, also?
Today's apes are primarily forest animals but if we try to claim that behavior of the 21st Century in the Year of Our Lord has evolutionary roots dating back 6 million years ago, that is just as much a statement of faith as stating belief in one God the father Almighty, creator of all that is, seen and unseen.
We cannot know properly how Neanderthals or australopiths acted given that the first view of chimpanzees was as pacific animals in comparison to humans while today books like Demonic Males scapegoat both men and common chimps for all that is evil in the annals of human history, while women are of course perfectly pacific individuals who never so much contributed in the least to human violence or the history thereof. And this is actually not a strawman take on Demonic males, either.
On another level, I find it highly telling that anthropologists and archaeologists prior to World War II were extremely interested in the history and development of war and warfare as an ordinary aspect of human history and prehistory, but nowadays we have such things as making the Mayans pacifist until we deciphered their script and it turned out these jungle hippies of scholars' imaginations were in reality just as bloody as Montezuma's boys if not more so. I wonder to what extent this reflects that Europeans were treated for much of the 20th Century the same way the colonial subjects they had the world over were treated? Why are archaeologists and historians so reluctant to realize that if the Iceman carried an axe he wasn't carrying it for money but because he expected to use the damned thing? To what extent was John Keegan correct in noting that no historians or archaeologists like to call prehistoric forts forts?
So then, I will ask those in this community, to what extent is it simply a political agenda to claim that Neanderthals and Orrorin tugenensis were in fact perfectly pacific animals without so much as having ever once shed blood in war the way we nasty humans do or alternately to make the reverse error as Wade in Before the Dawn does and assume they were far more warlike than the realities of the Pleistocene would have allowed for?