Actually I think the only a few owned slaves is a canard
Only a few owned a lot of slaves....but I think at least 30-40 percent of white families had at least one slave
One of my great great granfathers only owned one family of slaves....who worked alongside them
A smallish cattle operation in Smith county MS
and again another canard....small slave owners tended to treat them better
They were a bigger investment to them
I don’t look at it so much as a canard than I do a different interpretation of census records from 1860.
Here’s a good resource from someone who’s gone through that data.
http://fisher.lib.virginia.edu/cgi-local/censusbin/census/cen.pl?year=860
The 6% comes from number of slaves and number of southerners calculation as a whole. The author says this is specious because not all southerners had the means to own slaves. He also notes the age and sex groups. He breaks the southern population into age and sex categories and then comes up with numbers for some states like you cite. MS being the worst at 49% - all this on straight calculation of 1 slave per southerner.
You can Google or Bing all over the web and come up with 5%, 6%, 21%, 25-30 (from “From Slavery to Freedom”, to the numbers cited by the link I provided.
I don’t think we’ll ever know concisely for a number of reasons:
1) This is a question founded on political and ideological beliefs and data can be manipulated thusly,
2) Places like Wikipedia (in various forms) provide ‘answers’ all over the place (from 6% to 30%) - the ‘peoples’ dictionary, and
3) Many organizations that have been through the 1860 US Census data patently recognize the data are somewhat incomplete, brought on by various events around that time (e.g., secession, etc in 1861).
All I know for sure is that no one in my family which I have traced back to that era and before ever owned slaves - they were mainly too poor and were subsistence farmers at best.