I agree with you , the difference is incredible.
I have Hart, Shilen, and Krieger's, but I also have Remingtons that shoot just as well. The Remingtons took a lot of JB and elbow to get there!
Keep in mind the video was produced for a reason. Still, all in all, if I were going to build a custom gun on a Rem 700, Ed Brown, Jarret, or other custom action, I sure would go for a custom barrel too.
I think the real difference is making barrels for the masses versus the custom market.
It isn't cost effective for Remington, or others. Look at the new Rem 710? --no don't.
I can't imagine what one of those looks like through a bore-scope. I also know from shooting competition, that the custom steels and throats are MUCH better and last longer if properly cared for. Properly is another topic in itself!