Leep, here's how the 1/3 of the south had slaves numbers work.
A) In Alabama it's somewhere between 30% to 40% of white families had slaves (so yes, about 1/3).
B) A family is counted as owning the slave even if only one person did (i.e. the husband/father). I guess that's fair, like today saying our family owns our house even if it's in only my name and not my spouse's too and certainly not owned in my now grown kids' names.
C) A family is counted as owning slaves in all generations even if the family tried it for just a few years and decided it wasn't their cup of tea and freed the slaves (or their fortunes changed and they had to sell the slaves). This happened a lot. My family in Alabama never owned slaves (my mother's the descendent of sharecroppers from another state and my father is from a northern part of Alabama where slavery was practically non-existent even in farming communities like the farm my father grew up in). But let's pretend I had one ancestor who owned a slave or two for about 3 or 4 years and decided he didn't like it and freed the slave, and that was the only slave anybody in my family ever owned. That one event by one person would make my family counted as a "white family that owned slaves" even if almost the entirety of my family's existence we didn't own slaves nor wanted to. It'd be analogous to defining a family today as a "bank robbing family" if only one person in the family robbed a bank in the 1830's and it was only once in his life.
So think about that from now on when you point out or hear that 1/3 of white southern families had slaves. That's accurate, but within context that's not like what it sounds.
Was that really much of a factor though? It seems like it would be much easier to take a snapshot based on the census records for one year than to run through multiple censuses or other records.
Also, the more common experience, might have been to pass slaves on to relatives. Slaves were also rented out. So two families, one which had no slaves at home and one which owned no slaves might both be in a sense slaveowners. Families or individuals who had owned slaves once and expected to own them again might be more common than those who had sworn off slaveholding forever.