Completely my opinion, and a little bit of a rant:
The problem with a lot of small, private rescues for whatever animals is they're started and run by people who can't or won't make the difficult decisions about what animals are truly adoptable and end up taking in lots of animals that will never find homes, and that ends up sucking all their resources dry to the point they can't then take in the adoptable ones. To run a successful rescue, you have to be pretty ruthless about evaluating the animals and their chances of successful adoption. Admittedly, I would not want to be in the positon of making those decisions on a regular basis; it would be a brutal job.
If the case of my sister's and BFF's adopted dog horror stories, if the rescues had accurately represented the dogs the dogs would have never been adopted. And I'm sure it was some sweet, well-intentioned person who couldn't bear to see the dog put down and thought my sister or BFF was such a devoted animal lover that they were the animal's best shot. (My BFF eventually had to have her "bad rescue" put down)
The local equine rescue in my area is in exactly the position described above - it takes all their resources and more to maintain the herd they have now, the great majority of which will never find homes.
Maybe, but remember, what you consider "not adoptable" is different than what others consider not adoptable. I know a person who had a dog with spay incontinence (unknowingly adopted them that way) and kept the dog her whole life. I also know people who deliberately seek out dogs who have physical issues or senior animals, because they have the resources and will to help those dogs. There are rescue sites dedicated specifically to finding homes for disabled animals. As my dad the car salesman says "there's an a$$ for every seat."
BUT, rescues NEED to be honest about the health issues the dog may have. It's just wrong to misrepresent them to unsuspecting adopters.
I think it also depends on your definition of "successful" in terms of as rescue.. Is it to have the highest turnover possible? Finding homes for animals you think deserve a second chance, regardless of how much time it takes?
Personally, I think one of the benefits of the small, private rescue is that they can focus on a particular area of need rather than having to be ruthless like shelters do. If they have a thing for deaf dogs and want to focus on pulling deaf dogs from shelters, fostering them, and finding them homes (and there are homes out there for deaf dogs), then more power to them as far as I'm concerned.
My biggest issue actually is not with health, but rather with temperament. While most rescues will ruthlessly either refuse entry to or PTS human aggressive dogs some will not, and I do think that is wrong.