I believe the majority of southern free blacks who owned slaves were family members. Here’s what would happen.
A black man might be freed, then spend years gradually saving the money to buy his wife and children. When he succeeded, the often large fees associated with emancipation (in hopes of discouraging it) meant they often kept their family members in a legal state of slavery to Dad.
There were also a few free mulattos, mostly in LA, who had extensive properties inherited from their wealthy French descent fathers. The French had different ideas on this issue from anglo-Americans.
I think you’ll find that is the case in small numbers, but as you might take note from the small number of links I provided it disputes your given percentages and shows some historical facts taken from census counts at the time. It also shows a number of blacks who owned numerous slaves to run their plantations.
Please provide some proof to backup your given percentages. I would be interested in seeing the sources.