Brad, check these links.
https://www.youtube.com/watch?v=7duvo7XLWIshttps://www.youtube.com/watch?v=aII2tbavKnMThe first one shows how far the bore centreline can be out at the muzzle. The measurements for this operation were taken from the bore not the outside as the bore rotates on centre in the chuck and the OD looks like it is off centre. This is a separate but similar problem to barrel curvature. We still need to know where this bore centreline will point when your barrel is screwed in. So it is imperative to take bore measurements not outside diameter measurements.
The barrel is screwed in based on the breech operation shown in the second video because you have to start a bullet straight.
The second one is one by Gordy Gritters taking measurements from the bore before he cuts the chamber and it does not show where the muzzle will be pointing when it is released from the spider as it would sit in your action.
However you must take measurements again on the muzzle from the bore when you release the spider to find the highest part of the bore as the barrel would sit in your action. This is necessary if your barrel curves and OD is still concentric with the bore as in most cases or in the case of the bore not being concentric with the OD as depicted in the first video. As I said its tricky to keep a barrel from moving away from the established breech alignment when you release the spider to take muzzle measurements.
If you have never operated a lathe its easy for others to skip steps they take for granted.
Firstly, the bore needs to point up for compensation considerations whether the bore is offset or the barrel is curved (two different scenarios). I have had barrels where the offset is greatest at the breech and because they were chambered at the breech it gives the appearance the rest of the barrel is really bad. In the case of an offset bore from outside diameter, the belly created by the bore offline acts like a keel on a yacht. So the belly is effectively a counterweight. You want that counterweight swinging in the vertical plane. If it is at an angle the groups tend to arc more as you increase or decrease velocity. It is easier to tune vertical with powder charge if the bias is in the vertical. The old adage used to be, more vertical more powder. Secondly, the scope with a 12 o’clock orientation uses less adjustment.

I would like to add that fluted barrels pose a greater risk to accuracy if they are not cut concentrically with the bore and this would be my thinking based on the first video. Most barrels are bent and some bores are not concentric. I am reminded of an Australian Team to South Africa where some with fluted barrels failed. It was found that on the crook barrels not all flutes were cut to the same depth. The would obviously walk as the barrel heated up and even if they were in the correct orientation little would save them. Like a lot of teams gone by, the final gear preparation is done at the last minute and bugs so obvious to some are not picked up. So I applaud Peter and DaveMc and others for their meticulous preparation of a couple of years to knock off that world title. The corporate knowledge has to be remembered so mistakes are not repeated when it counts and it has to be shared so new blood can increase the talent of future teams.