This idealized barter economy contains a the same rather specific notion of value (as something countable, comparable, fungible, etc.) that is like the idea of value that a monetary system rests on. The article suggests that historical evidence fits better with the idea that money actually precedes that notion, rather than the other way around. This should impact the way barter economies are analysed and compared to monetary systems.
Graeber is an interesting guy, but he is also a Socialist with an agenda.
I remember a story of a linguist (Dan Everett, probably) working in the Amazon. He tried to convince a speaker of the language he was studying to sit with him for a few hours to help him with his grammar. He offered some fishhooks in return. The guy asked, "do you fish?", to which he replied no, and then the guy looked puzzled and said "then why don't you just give me the fishhooks?"
There are all sorts of societies, or were, throughout history. I remember reading about one where they didn't have the concept of ownership of things. But it was very logical for their environment, where most things would only have been a hindrance. In such a society, for example, maybe people would be wondering why somebody would want to hold on to fish hooks.
So sorry, some anecdotes don't cut it.
Me having an agenda: I have an opinion, obviously. Feel free to take what I say with a grain of salt. My whole point was that you should also take what Graeber says with a grain of salt.