I think I see where you're coming from on this.

That American fascism took some ideas from Austrian economics isn't surprising. Hitler drew ideas from Nietzsche's work and Nietzsche would have been horrified if he'd lived to see it. But authoritarian fascists drawing on some of the ideas of liberalism doesn't make them liberals. They lose any claim to being "liberal" once they abandon the core value of freedom.

And yes, fascism was aiming to be a third way between liberalism and communism--authoritarian capitalism, with the authoritarian portion supreme. But that is not what liberalism and libertarianism are supposed to be. If they're capitalist AND authoritarian they are really fascists no matter what they call themselves.