Here are some pics of the burr being removed. It's a new case that has been trimmed in the Giraud after being sized and run over a mandrel, and has had the K&M VLD chamfering tool remove the remaining burr form the inside of the case mouth.

The neck turning tool only removes material around the case mouth. It's not touching the neck after that.

You can see the ring of material that's been removed.

A few twists in a Glit pad and the outside is the neck is nice and smooth.
I got the same thing when I tumbled with SS media and I could see the difference with my pressure trace system between the cases that had it removed and those that didn't. The rifle also shot better when they were removed. A fraction of an MOA better, but noticeably better.
I beleive that removing this burr is often the reason why people see accuracy improvements after neck turning. It improves neck tension consistency, but not for the reason that is often attributed to it.
You often hear people say that they don't see any improvements with neck turning in loose factory chambers, but they do in custom chambers that are supposed to be no-turn. Many no turn chambers are only 0.004" more in diameter than loaded neck diameter. All that it takes is 0.001" of burr on the inside and on the outside and you have a little ring of brass that is being pinched between the bullet and the chamber. And I highly doubt the burr is going to be consistent from case-to-case, so on some rounds it may not get pinched, on others it may just touch (but will interfere with the pressure ring on the bullet), and on others it may be getting pinched hard.