I apparently have the advantage of having a machinist's square, and know how to use the depth gauge of a caliper to square a edge of any tube to the inside of the barrel. I don't think there is any mystery, or great skill to doing so.
Using card stock, without FIRST marking your masking tape with a ruler or tape measure measuring from the breech of the barrel would have you relying on the cutting of the outside of the barrel being "plumb " to the bore. You are correct in that this would be a false assumption. It may be plumb, but it also may not be. It all depends on who made the barrel originally. Its less likely that the breech end of the barrel has been cut out of Plumb with the bore.
I use either my machist's square, or, in a Pinch, my caliper's depth stem to check the square of the bore to my muzzle during final filing.
The Proof of the pudding, so to speak, comes in firing the gun with its new muzzle. If its a shotgun, a Non-square ball will throw both shot and RB loads away from the POA. Filing the muzzle on the side of the barrel in the direction to which the ball or pattern is thrown, will move them back to POA. Even a lathe will not put a RB or shot pattern on target with POA on a barrel that is not plumb bored. If you do support a barrel in the lathe at both the breech, and then just behind the muzzle, you will see how much "Drift", or run-out" shows at the muzzle. The only way I know to use a lathe to square the end to the bore is to use centers at both ends of the pipe. That should have been done when the outside of the barrel was turned, or machined.
I have used the center in my tailstock to allow me to cut through the barrel most of the way, but not through, so as to not endanger cutting that center. Then the barrel is removed, and the cut is finished with files or saws. If the bore drifts at the muzzle, I at least know what is needed to be done to get the barrel shooting to POA.