As much as I'd like to believe in no-kill shelters, I can't. No-kills are simply unsustainable because there are too many animals without homes. Over 6 million animals are left at US animal shelters annually-- there are too many of them to re-home. Half of them are euthanized, but no-kill shelters are too busy keeping their hands clean rather than addressing the problem. True no-kill goals can only come from spy-and-neuter programs.
In all honesty, I have very mixed feelings about peta. However, the ruse about their adoption rates vs euthanasia rates is a half-truth concocted by CCF, who by the way owns the website you've linked to. https://www.sourcewatch.org/index.php?title=Richard_Berman_cares_about_animals:_clients_exposed
CCF is a front group posing as a 501(c)(3). It has attacked such diverse groups and individuals as the Alliance of American Insurers; the American Academy of Orthopedic Surgeons; the American Medical Association (AMA); the Arthritis Foundation; the Consumer Federation of America; the Harvard School of Public Health; the Marin Institute for the Prevention of Alcohol and Other Drug Problems; the National Association of High School Principals; the National Safety Council; the National Transportation Safety Board; the Office of Highway Safety for the state of Georgia; Ralph Nader's group, Public Citizen; the Centers for Disease Control (CDC) and the U.S. Department of Transportation (DOT).
Peta is not a traditional shelter by any definition. They provide euthanization services and these numbers are folded into CCF's "adoptable animals" numbers. If you believe that euthanasia is not preferable to shooting/ running over with a car/ abandoning animals, that's your call.