To be frank, it's more like "they were capitalist because the state privately owned the means of production," provided the critique is attempting to demonstrate that the society was actually capitalist rather than subject to the contradictions of international capitalism in the first place. Trotsky for instance shies away from describing the Stalinist USSR as "state capitalist" but rather approaches the matter through the lens of permanent revolution which regards capitalism as an international system subject to constant pressures, through the form of incentives, towards expansion into new product, resource, labor, and commodity markets. It's really a generalization of the understanding of imperialism as international continuation of local bourgeois interests by force against the local bourgeoisie of other nation-states and pre-capitalist societies. As with the Paris commune, Catalonia, and so on which collapsed not under the weight of their own contradictions but by active subversion by foreign powers in the name of bourgeois interests, and those places who resisted this subversion to varying levels of necessity with authoritarian rule or fell to authoritarianism through this justification, we cannot stably cordon ourselves off in some corner of the world and declare capitalism to "not exist" there, without actually solving it on the grand scale.
IF, however, you mean "communist" in the sense of the hypothetical end of history where classes, money, and the state have ceased to exist, rather than "communist" in the sense of the proletariat organized as the ruling class, the existence of bartering is indeed evidence that not all goods and services are freely given and received, so yes. But there's nobody who has ever seriously contended that the former state of affairs has ever been reached, so the point is moot.
It is another equivocal fulcrum that the right relies quite heavily upon, however, arguing the unsuitability or impracticality of one and proceeding as if it was proven about the other. It's unfortunate that any and all attempts to point out this fallacy as a disingenuous rhetorical sleight of hand is itself perceived as disingenuous.
Here you radically misunderstand Marxist epistemology. "Capitalism" is not a totality, it is not defined as "the current, all-encompassing state of affairs, whatever that may be" but is instead defined objectively as a specific way that the social relationships around production are structured, and then analyzed for its implications for, influences upon, and role in forming "the current, all-encompassing state of affairs, whatever that may be." This is what we mean by the "materialist conception of history." The totality can only be studied and comprehended in its specific character by looking at the principal factors which demonstrably shape it and how they do so, not by heuristically manipulating this totality itself - as the postmodernists have settled upon in rejecting "meta-narratives" about reality.
This is, unsurprisingly, yet another equivocal fulcrum the right makes use of. For example, if I were to make the definition
>We are said to live in a capitalist society if we inhabit a society of some sort in which capitalism exists
it is clear that the first instance of the word capital* refers to the totality which you describe, i.e. some society itself at large, being the actual phenomena of social organization around production together with those remaining elements of society which they influence and those which they do not, and that the second refers specifically to the manner in which the social relations are structured. So "capitalism" is at times meant as the concept, and at others as societies in which it occurs, but this is always clear from context. Substituting one for the other (see above,) as you have done here, is another unfortunately common use of the same fallacy.
Honestly though most Holla Forumsacks and liberals who come here to argue aren't even aware of their implicit reliance on the argument structure you've provided here, and I commend you for that and for coming to argue in good faith. We appreciate it