The German State absolutely seized the means of production, for example taking them from Jewish businesses and then "privatizing" them to NSDAP loyalists. Business interests that were not stolen outright were subject to quotas, regulations, state approval to hire or fire and various other controls. In short, the nominal owner did not exercise the power associated with private property. The "owner" (in the sense of having the choice of how to use or dispose of the asset) was indeed the State.
Here is a lecture on the topic:
