I think it's just one of those things where the person/"rescuer" feels better about themselves/more legit in their work with their horse/they feel like they're making a difference when they say their non-rescue is a rescue.
Also, I think "rescue" means different things to different people. To me, and it sound like to you, it means saving a horse from immediate physical/emotional harm. To others, it means saving a horse any sort of harm, whether that's harm that's happening now or harm that may or may not happen in 6 months.
Sometimes I say I "rescued" Lacey, other times I say I "got" her. Most of the time I just say I "got" her but then I share about how she was a week away from being put down and how her previous owners emotionally mistreated her. Sometimes though, I don't want to say that whole story but I don't want people to think that she's just a perfect little princess that I trot through daisies 24/7 so I say I "rescued" her.
At least in my area, with the people I meet, they seem to think (if I just say I own a horse) that I'm some sort of spoiled rich kid, which really couldn't be further from the truth, so if I imply that Lacey has issues by using the code word "rescue," they seem to give more respect to me as a horse person. Which is kinda selfish but effective. Haha
And I would like to point out, in response to your statement that "Or they say that the horse was untrained or poorly trained or abused before they got and now it is all better and perfect all because of them," that that's not always necessarily a non-truth. I agree that some people are completely too liberal with their definitions of "issues" or whatever and use them to describe every horse that's not dead. However, it is true for some people. Take my favorite subject, Lacey, as an example, she did have issues: she could not walk under saddle, she reared, she bucked, she spooked at everything, she ran people over while they led her, she was herd bound, basically she had every nasty trait in the book besides biting. And yknow what? After I started working with her, she has become "perfect." Of course, I think that has less to do with my training prowess and more to do with the fact that she needed a leader and that I stepped in quickly and gave her strict rules to follow which was just what she wanted. So she became "perfect" through her belief in me as the leader. I also have no doubt that if I disappeared and she had no leadership again, she would revert right back into those old habits.
Was that what you wanted to know?
Great post wild_spot! "Abused" or "rescued" horses have absolutely no reason to not behave. It might take them a bit longer to be able to have their halter put on without drama if they've been severely beaten in the face or something, for instance, but someone should be working on that with them and not just saying "that's the way they are."
People are dumb. Heehee