Counting up the problems:
(1) How do we know what they thought and whether they shared? Answer: by analogy with primate species and modern-day hunter gatherer societies. So that's suspicious, but I'm not disagreeing with it.
(2) Did not store or hoard: well, no, given that they lacked the technology to do either, unless they didn't but either way, we don't know _this_ either.
(3) Egalitarian behavior: if there is a general rule out there, it's that communal ownership arises in the poorest, most resource starved groups -- not the ones with no shortages.
How do you pack that many errors into _that_ short a sentence? It isn't even unclear. It's very clear. It's just very wrong in every possible way.