Literally the national guard brings government surplus food to food banks and the VA is the only socialized healthcare Americans have experience with. I see how they get the impression.
I think the fact that I was a military kid is a major reason why I'm drawn to socialism over capitalism. Authoritarian socialism is the big scary bogeyman of American culture but... that was my childhood and while not perfect, it was a lot better from my perspective than the dumpster fire of civilian America.
Centralized/state control versus pure corporate profit seeking. Of course, there's still the grift of capitalism going with war profiteering weapon contractors. You can't literally buy stocks of US military though.
Socialism is an economic system in which workers own the means of production. It has nothing to do with centralized planning. If it did it would be to say our anarchist comrades aren’t socialists!
The US military is centrally planned, by and in service of a dictatorship of the bourgeoise— the capitalist class who own the means of production and control the government, and use its institutions to further their interests. Thus it is definitionally a capitalist institution. These are, in fact, the people who would try to kill you if you attempted to install socialism by seizing the means from the capitalists.