I think that we are talking about a couple of different situations here, what you can get away with on a hunting, rifle and what you are about when mounting on a pull out all the stops competition rifle for something like benchrest or just the fun of having a full house competition grade rifle. And then there are those who approach the building of a hunting rifle with all of the seriousness of one built for the highest level of competition.
Another thing, I don't think that anyone who has not done a serious amount of ring lapping for a lot of different situations is really qualified to make recommendations, although their recounting of what they do and have done is of course just fine.
The only way that you can see how even or uneven a scopes' contact with rings is, is by making a few strokes with a lapping bar to see where it is cutting and where it is not.
Even if the rings are the best, and one is using a one piece base, if you screw that base down onto an imperfect receiver it will bend and take your rings out of alignment. Also, there is some distortion that can happen when you tighten a ring onto its base.
One of the best smiths that I know of, Speedy Gonzales once told me that he generally laps to 50% contact and then beds the rings to the scope. Also If you read Tony Boyer's book his scope mounting procedure is quite involved and exacting.
As others have said, I wish that Burris rings would cover all the bases, but until they do, I will not be just be bolting things together and calling it good enough.