Largely correct. Communism is only compatible with true anarchy, that is, the voluntary cooperation of people who are in no way coerced by a state power. Capitalism on the other hand is compatible with a wide variety of forms of the state, whatever best serves the needs of the exploiting class at a particular stage in its historical development in a particular nation. It is just not compatible with anarchy (of a true nature, not the rule of bandit gangs called “anarchy” by bourgeois propaganda) because it requires coercion to maintain the exploitation inherent to capitalist production.
But capitalism is not based on “economic theory,” it is based on historically conditioned class rule.