I think you’re missing a “no” here.
Anyway, of course even under the CCA comics censorship was self-imposed – the Authority was a creation of the comic publishers, and funded by them, and no publisher was ever required by anything other than their own horse sense to submit an issue for review. Although in the early days shipping without the CCA stamp was the kiss of death, because distributors would refuse to ship it, and stores would refuse to stock it. That hasn’t been the case in most of the country for decades now, though.
I don’t think Image or Dark Horse (the #3 and 4 publishers thru comic shops) ever belonged to the CCA, nor did CrossGen (briefly the #5 publisher), even though CrossGen’s stuff would have been approved without any agita.
Archie Comics, I think, still gets regular CCA approval. I expect it’s only a matter of time before DC stops submitting issues to the CCA altogether, except maybe their kids’ titles.