Just to clarify, the angle mentioned has the rifle as its vertex and the width of the group is a chord that subtends some angle. At 100 yards, one inch subtends an angle of 0.955 minutes (0.955 60ths of a degree).
This is not intuitive to everyone, so think of it this way: Suppose you put two holes on a 100 yard target an inch apart. Further suppose there was a second target behind it at 200 yards. If you could look through the center of your sight at the first hole, you could draw a straight line through it to the 200 yard target. Now suppose you looked at the 200 yard target through the second hole and drew a second straight line through it. You'd have to move the rifle slightly to put that second hole in the center of the sight. That slight movement represents a small change in the angle at which you are viewing the target, assuming the rifle pivots around a fixed point on the bags. So the two lines you drew would meet at that pivot point (the vertex of the angle). But because the sides of any angle diverge in proportion to their length, you would find the two lines met the paper on the 200 yard target twice as far apart as they were on the first line.
You can actually try that experiment, by the way. Put up a 200 yard target and put a 100 yard target right in front of it that is half the size so you can tell when the two are lined. With a typical high power rifle cartridge, you will strike find the bullet drops a couple of inches between the 100 and 200 yard targets, but will hit both and let you see the dispersion. It is best if the 100 target has a big hole cut out of its backer where you are going to shoot it, so only the thickness of the paper affects the bullet. Going through something heavier can introduce some deflection drift. Plain paper won't have a significant effect at the ranges we're talking about. Bryan Litz did this with bullets flying to 1000 yards without incurring trouble with the process.
If you try the experiment, as already explained, a 1" group will normally actually be slightly over 2" at 200 yards owing to drift components having increasing amounts of time to act over each successive 100 yards. There are some funny circumstances in which that may not occur and randomly some drift factors can work to tighten the group, but that's not as common as the reverse.