Okay, now I see it. I still think the diagram is poorly made, but the end of the first sentence should say, "depends (as a first approximation) on the ratio of the sphere's diameter to the distance from the sphere." or something like that. Yeah, subtended angle (which is what he highlights in the 2nd sentence) depends on more than distance.
Bad Astronomy had a good picture of a planetary nebula that was 2 AU across at a distance of 500 LY. It was kind of fuzzy, not nearly as pretty as some Hubble pictures of other planetary nebula, but they were 4.3 LY across at 10000 LY distance. but when you compare the angular sizes, the quality of the first becomes dramatically impressive (13 milliarcseconds versus 1.5 arc-minutes).