There are a lot of ways to chamber a rifle barrel. All of them can work if the geometry of the barrel blank happens to match the method chosen. Only one works, in theory, pretty much regardless of barrel blank geometry. That's the one in the Grizzly video. It aligns the breech threads, shoulder, and chamber, with the segment of the bore that is the lands and immediately after the lands. Done correctly, that assures those elements are aligned. Other methods can result in them being aligned, or possibly not misaligned enough to matter, but in general they aren't theoretically as correct.
I have used a slightly modified version of the Grizzly video method including pre-bore on a number of rifles and they all shoot tiny little groups. Other folks have used different methods, including the zero both ends method with the breech clamped directly in the chuck jaws, and had barrels that shoot tiny little groups. The chuck jaws turn the centering of the far end into a barrel bending exercise.
I use a ring of #6 or #10 copper ground wire around the breech to hold it in the 4J. Same on the other end where the cross head screws will contact it unless I tape the barrel first.
This is my through the headstock chambering setup:
Note the dial indicator on the tail stock for measuring depth.
This is my home made reamer pusher:
If anyone is interested I can explain the theory behind the design and how it was made.
The hardest barrel I've done was for my wife's sporterized 1903 Springfield. Her father had the rifle built for her in the fifties. The bore was destroyed when someone fired surplus ammo with corrosive primers. It was a challenge. Square threads right to the barrel shoulder weren't too bad. The hard part was figuring out how to perfectly align the extractor groove in the end of the barrel so it fit perfectly when the barrel was torqued in place. Once I figured that out and found the nominal dimensions it came out really well. This shows the setup for cutting the extractor groove. I torqued the barrel with the completed chamber into the receiver, held the barrel in my home made barrel vise, indicated it until the bottom of the receiver was parallel with the mill table, tightened the vise, removed the receiver, and milled the slot. When I torqued the receiver back into place and reinstalled the extractor on the bolt, it all fit (and I resumed breathing). This is the setup for cutting the extractor slot in the breech of the barrel:
Setup:
Cut done (it had to be done upside down to avoid a climb cut which would have been a disaster):
It fits:
Fitch