I read the linked post twice, and unless I missed something, it seems like they've just moved the different sections (A, B, etc) location on the form around.
"...In those regions where carry permit holders are not required to undergo another NICS check, a 4473 still needs to a completed."
In regards to the above paragraph, Kentucky [currently] doesn't require CCDW carriers to go through a background check. However...where I usually get my ammo locally across town, I asked the store clerk once that I had my CCDW permit, and if I were to buy a firearm there would I need to go through the background check. He said they didn't recognize KY permits, even the store is in KY, because their home office is located in Illinois, and they go by the home office regs.
When I bought my recent firearm, I went to the Army base PX. It's a 45 mile drive one way, but I like the tax savings, and they have a decent selection of ammo on-hand. Anyway, when I went to purchase the pistol, I mentioned to the sales clerk that I had my KY CCDW, and could skip the background check. Nope. Still had to do it, but it seemed to go much quicker.