That's what it means, literally. Ask anyone that works at my cooperative what it means, they will tell you the same.
I'm glad your group is finding a way to make it work at the micro level, but at the macro level, it's going to be a plutocracy with a bunch of oligarchs that operate the nationalized monopolies. It might not be the case that you couldn't finance your business' capital goods and eventually own them, but in true communism you will simply be unable to play the game independently. The government will seize capital and represent a behemoth against which you cannot compete.
Your co-op works because it's relatively small and (presumably) full of people of like mind. Unfortunately, governments of size will always be corrupted by the one constant in all governing systems: human nature.
Communism and international socialism often look good on paper. But in practice their governments are corrupt, non-representative, and tyrannical. They get hijacked by an oligarchy who is in it for themselves only. Which leads to suffering for everyone else. Exactly like what's festered in the USSA.
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