Hmmm, the Nazis were nether left or right but the 3rd way.
No doubt companies were well regulated and clamped down on hard when they let greed get in the way of national interests (and capitalism needs loads of regulating, as we have been recently reminded). Then again, companies that collaborated got away with murder.

I think it fair to say any socialism was over shadowed by other characteristics and it is quite bizarre that should be singled out as the defining feature.

Give it another 2000 years and the Nazis will probably be admired for all the straight roads they built in europe or some such. If we learn anything from history, it is we dont really learn anything at all.