No that's not accurate. The brain may not be able to distinguish the two focal planes but it's just wrong to say "the brain interprets it as a 3rd, or 4th or 5th plane".

And this Facebook technique clearly doesn't use the same technique. Instead of a focal plane they have a focal surface that isn't restricted to a plane. It might not be noticeably better (who knows) but it's definitely not the same technique.