I had a professor who wrote like you once.
Once...
Besides, I don't think we know enough about primitive cultures to determine their relative respect or disrespect for private property and their relative socialist or capitalist natures. 'Capital' as it stands has existed since man produced something not with an eye to eating it or satisfying some other immediate want with it, but toward the future and how it would help him produce more or more easily what he needed to fulfill those more immediate needs. In the strictest sense once man realized he need not look for sharp stones and sticks but could make them himself, capital accumulation began. It wasn't very long lived capital, but it was there. Replacement costs can be a bitch.
Once...
Besides, I don't think we know enough about primitive cultures to determine their relative respect or disrespect for private property and their relative socialist or capitalist natures. 'Capital' as it stands has existed since man produced something not with an eye to eating it or satisfying some other immediate want with it, but toward the future and how it would help him produce more or more easily what he needed to fulfill those more immediate needs. In the strictest sense once man realized he need not look for sharp stones and sticks but could make them himself, capital accumulation began. It wasn't very long lived capital, but it was there. Replacement costs can be a bitch.
Indeed, the so-called "pre-capital" societies are appreciably more difficult to categorically analyze than contemporary societies: while the means of value production - mostly agrarian in nature - were most certainly collectivized, such means were subordinated to the wishes of the highest class strata, and; contrarily, currency also existed as a relativizing commodity, but was most primarily a method of exchange, rather than a value creator itself [vis-a-vis being so-called, "money capital", with the technical-rational taxation systems adherent thereto].
In compounding this confusion, however, the more advanced classics [see: Indo-American, Egyptian, Romans and so forth] most certainly had interest and tax systems, necessarily positioning capital [whether in money-capital or private property] as the determinant form of self-enlarging value - the key characterizer of capitalistic economies. So, as you have said, characterizing all pre-industrial societies with one broad, negative stroke may be presumptuous; however, I did not - the word "derivative" was meant to precisely encompass a wide spectra of social organizations that, ultimately, can be considered in regard to their determinant method of value production in an aggregate fashion, and the relative position to capitalism or socialism *.
It appears you have analyzed the distribution of the social capital as the primary determiner of an economic system's label, where I am more primarily concerned with its mode of production; and, further, you seem to be extrapolating the microscopic perspective of exchange to the macroscopic context.
* I say aggregate as value production, distribution and exchange on the level of the individual firm involves microscopic imperatives such as coercion, power, status and so forth that obfuscate their nature; as a result, modes of value production must be considered in the aggregate.