My example seems fine to me. Without 1:1, a 16:9 source will get stretched to fit the screen. You assumed I meant only stretching vertically. He wanted the most simple explanation and that's what I gave him.
I don't take issue with your definition of 1:1 mapping; I take issue with your statement that without it, a 16:9 (or 4:3, 3:2, or other aspect ratio) source would be stretched to 16:10 to fill the screen. A 16:10, 1920x1200 display without a 1:1 mode but with a properly working aspect-scaling mode can scale, say, a 720p source correctly with black bars on the top and bottom. The 1:1 mode would display a 1280x720 box in the middle of the screen.
The problem with the BenQ is that its aspect scaling does not always behave as it should, so the 1:1 mode, particularly with a 1080p source, should be an easy way to force correct behavior. Unfortunately, it doesn't look like its 1:1 mode behaves well all the time either.
Sorry for nitpicking, but the problems with the BenQ surface in pretty specific situations and your example did not specify the circumstances where aspect scaling would not work properly.