Before you call me out for spreading misinformation, might I recommend reading the page where I obtained me original information?
It's the government's ADA FAQ page.
The uses you described in the rest of your post are covered because, as you said, the animals are performing a specific task that assists the person with the disability. I have absolutely no problem with this at all. What I was describing were "Emotional Support Animals" that are only with a person because they calm them down. My dog calms me down, too, when I'm upset or feeling down. I'm not bringing him to WDW and demanding an exception to the "No Pets" rule. If your animal is a legitimate service animal, you need to show a card or something that verifies it. It doesn't, and shouldn't, have to state what your disability is, but it is proof of the legitimacy of your animal. You show the card, your dog goes through. Don't have a card? Time to board Fifi.