Do you have a particular example of a country that has a centrally planned economy and doesn't allow for private ownership of the means of production? (with the exception of North Korea)
The list of countries that are actually socialist is small after the fall of the Soviet Union.
...and continues to shrink.
For instance, even Cuba started making the transition about 8 or 9 years ago to start allowing private sector businesses to open, and if I'm not mistaken, finally started recognizing the concept of private home ownership. However, Cuba (and Belarus) still have a situation where their public sector size is still around 70%.
China has increasingly been making the move toward a more mixed economy over the past few decades.
Vietnam started allowing for the concept of "public-private partnerships" for businesses in certain industries (granted, they still only allow one business per person).
Laos has also been moving in that direction as well and in the late 80's, started encouraging some private sector activities. (however, the government still maintains control of the critical ones...so in that regard, it's still very much centrally planned for the most part)
It also depends on which means of production are being referred to, and how much of it is "up for grabs" by the private sector.
For instance, if a hypothetical country maintaining overwhelming majority ownership of most of the means of production for all of the important/critical industries, but allowed the private sector a few somewhat trivial token ownership opportunities, I'd still say that's largely centrally planned. For instance, if a country allowed people to own their own small processing facility for some non-essential goods, or allowed a person to own a very small insignificant farm (while the government still owned all of the big ones), that would still fit the description.