Yes, the theory comes from the superficial observation that the actions of the nominal extremes look very similar. And when your head is being crushed by the boot of authoritarianism you don’t care if it is the right foot, or the left foot wearing it.
At one time there were many concepts of what Socialism is, and at the time nazism was A socialism, of course completely opposite of the concepts that survived.
Yes, I agree with you.
I just wanted to add that at the time “socialism” was any answer to the question “how to structure society so its members benefit the most?”
Nazism was such an answer, and it was “eliminate all who don’t contribute”.
Of course the concept of socialism later evolved and got more strict so that Nazism doesn’t count anymore.