As I explained, they don't run any adoption shelter. They run a free clinic for the poor they call a "shelter of last resort". To compare the euthanasia rate from a clinic to an adoption shelter is apples to oranges. By this standard nearly every veterinary clinic in the US would have a 100% euthanasia rate an a 0% adoption rate.

Didn’t they kill a child’s chihuahua for no reason?

This was a tragic, but isolated, event. It was ruled as a mistake by the prosecuting attorney who dropped all charges and eventually the family themselves admitted it had been a mistake after settling a civil suit for 1% of the damages they had initially sough.

The district attorney made it clear the event was primarily the fault of the owners who were breaking the law by allowing a small dog to freely wander in a trailer park without any identifying collar or a chip after having been warned that strays were present and soon all dogs without identification were going to be rounded up. PETA still fired both employees for the violation of their policies which led to the dog being put down.