What they got wrong is that Nazism is not socialism, per se.
The dictionary definition of Nazism is in fact socialism. The German name of the Nazi Party is 'Nationalsozialistische Deutsche Arbeiterpartei'. National SOCIALIST is literally enameled right there in the name!
I really didn't come here to argue po-tay-to vs. po-tah-to; if you want to use the establishment's false left-right narrative, go right ahead. For me, true right-wing politics (libertarian minarchism, anarchocapitalism, propertarianism) is literally the opposite of statism/totalitarianism whether the statists are Nazis/Fascists or Communists.
Oh, and if you REALLY want to bake your noodle, take a look sometime at the rostrum in the House of Representatives. What's behind the Speaker's chair on either side?? Fasces... as in fascist. Our government was hijacked a LONG time ago (100+ years??) and it seems no one's noticed!!