I am sure you are correct but Von Mises seems to disagree with you.
https://mises.org/daily/3274The second pattern [of socialism] (we may call it the Hindenburg or German pattern) nominally and seemingly preserves private ownership of the means of production, and keeps the appearance of ordinary markets, prices, wages, and interest rates. These are, however, no longer entrepreneurs, but only shop managers (Betriebsführer in the terminology of the Nazi legislation). These shop managers are seemingly instrumental in the conduct of the enterprises entrusted to them; they buy and sell, hire and discharge workers and remunerate their services, contract debts and pay interest and amortization. But in all their activities they are bound to obey unconditionally the orders issued by the government's supreme office of production management. This office (theReichswirtschaftsministerium in Nazi Germany) tells the shop managers what and how to produce, at what prices and from whom to buy, at what prices and to whom to sell. It assigns every worker to his job and fixes his wages. It decrees to whom and on what terms the capitalists must entrust their funds. Market exchange is merely a sham.
Murdock was more correct than I thought.