@bharvey2 your post was a bit hard to read (at least for me); some of it is black on a dark gray background.
Authority means "under that license". Not, "I gave you permission to use my repeater" but "You are a member of my family operating under my license".
I'm not sure how your question about (2) negates the need for a repeater to ID. It says that persons operating on a family repeater (which doesn't need an ID as long as 1 and 2 are met) DO have to ID. In other words, you cannot set up a GMRS repeater for your family to use and not have any ID at all (either by the repeater or by the users).
95.1751 states that GMRS "stations" MUST identify. (Stations include not only people talking on radios but also repeaters.) It then outlines the conditions under which a repeater does not have to ID ... in other words, unless those conditions are met, it DOES.
Am I "passionate" about this? Nah. I don't have a GMRS repeater, and don't ever intend to set one up, although I do use a couple. If I did set up a repeater, you can bet that it would ID as required by the rules.
My favorite new saying is, "There's what the FCC rules say, then there's what some people THINK the rules say, and finally there's what people think the rules SHOULD say." The rules say that repeaters need to ID except under certain narrow conditions.