Your confusing the act with the intention.
Nationalizing is left wing economic policy and is always justified under their banner. Why someone really does it is a different story, if we want to include alterior motives and conspiracy theory.
When THE state that is privately owned and controlled (like the nazi regime, the stalinist regime, or the czarist regime) and it owns property, it is a form of private ownership. Nationalization is only a traditionally left wing position if the state is democratic (i.e. alterable by the public) and the policy is implemented with a focus on the welfare of citizens and the people as opposed to world conquest which seemed to be Hitlers idea. So, no, you're utterly wrong.
The stalinist USSR was not left wing because it was controlled by a narrow minority of people, who owned and controlled EVERYTHING through the state which they owned as well. Their power was largely unregulated and they themselves were unaccountable, free to dispose of the nation and its resources in any manner they saw fit (at least in theory). Furthermore, Hitler did not nationalize everything, his economic policies were sort of centrist in that manner. Instead, he intigrated large parts of the capitalist class into the regime through lavish contracts and cartelization. He also destroyed the labor movement and so forth. Indeed, the big businesses had heavily invested in his political career.
The nazi state was privately owned and controlled, indeed the traditional bureocratic class was largely phased out, so this had great practical implications in governance. Instead of traditional bureocrats, who Hitler perceived as weak and otherwise unworthy, Hitler granted power to his
Gauleiters, or party buddies, who received their own turf (like an occupied country) and whose power was almost absolute like that of an unregulated private owner. Meanwhile, the traditional government institutions were becoming irrelevant.
For instance, I would say that Chavez's nationalization is under the left-wing economic banner... but he is probably only doing it for personal power.
Chavez is a different case, having been democratically elected several times (Hitler got power through backroom dealing and subsequently abolished the democratic public state). And furthermore, most of the economy in Venezuela remains under private control (more so than in many Scandinavian countries), even though Chavez probably could have run through a program of stalinism if had wanted to.