Interestingly my mental picture of this comes from the other direction.
The vertical trajectory plane is the constant. Thus, when you cant the rifle you just move the line of sight to the side relative to the trajectory rather than shifting the point of impact....
Alan
If I have understood you, I don't think that's correct. Though it amounts to much the same. What concerns us is point of aim vs. point of impact. What matters is the point of impact. In reality what we have control of is the point of aim.
My mental image is that the sightline of the 'scope should be absolutely vertically above, and also horizontally in line, with the bore axis of the barrel.
Cant alters this, resulting in horizontal stringing. As also does a 'scope mounting which is not absolutely in line with the bore axis, which is where good quality mounts, rails etc. matter. If they are only slightly horizontally misaligned similar things will happen. E.g. get a perfect zero, preferably at the second, not the first one (e.g. say you have the first zero at 100 yards and the second at 200), and except at precisely 200 yards the POI will be off to one side or the other.
Of course there are the old school types who consider that zeroing say 1.5" high at 100 yards is a universal method. I don't have much time for that. Enough to get you on the paper at further distances perhaps.
In the example I quoted, 1.5" scope height (that is optical centre of scope above centre of bore), using a zero of 200 yards. The primary zero will then be at between 25 and 50 yards. At 100 yards it will actually be 1.81" high. Quite how you could do that anyway with even a genuine 1 MOA rifle and determine where the centre of a group is to within tenths of an inch, I don't know. Much better to complete your zeroing at the secondary zero, even if it means you have to walk 400 yards every time you look at the target. or, better, use a spotting scope.