They're a private company the same way any company that is effectively funded by government contract is. Technically it's true, but they haven't demonstrated actual viability in the private market (much less profitability). And the achievements you note have little or nothing to do with their status as a private company and almost everything to do with taking advantage of government research from the past half-century.

The bit about Nazis is entirely irrelevant.

> The vast majority of government research for space launches was done by the Nazis

The extreme majority of government research for space launches has occurred since 1950. The extraordinary resources put into the US space program, including the research necessary, makes the Nazi efforts look hilariously trivial by comparison.

The key is to no longer take the fuel with you up there.