I have had the opportunity to be friends with shelter owners and rescue owners, kill and no-kill. I let their opinions be my guide. They all hate PETA because PETA euthenizises, as you say, way too aggressively.

The ones at no-kill shelters will often overfill to rescue an animal from a shelter they know is going to euthenize it. They often have lists of foster families who will take in animals with most "terrible conditions". I have a family member who fosters Feline Leukemia cats exclusively (it's contageious) and gives them a good life. Properly cared for, they have a solid chance to live well almost their entire natural span. And she always has room for more. So PETA putting down a cat with Feline Leukemia instead of finding people like her? Unacceptable.

The kill shelters I know people from? Last resort. Their kill rate is virtually zero because they start bugging their friends if they know they're getting overfull and have a hard animal to home, and that animal usually gets homed with one of the people who works there.

Both of them have relationships with larger-scale rescues. The larger rescues have aggressive foster farms that usually has openings for high risk dogs, and often have Animal Behaviorists volunteering that can help to find homes for animals with unique behavioral issues.

It's a lie to say that no rescue animal EVER has to go down. But the consensus of the people who matter is that PETA simply has never shown evidence of trying hard enough to save the ones that should be saved.