Jean Martin is absolutely right to say that killing of any being, other than to end unrelievable suffering, is not euthanasia by any uncorrupted definition of that word.
HSUS also uses the corrupted meaning of the word "shelter". Real shelters don't kill the sheltered.
HSUS may not be in the pet disposal business but for some reason it promotes the industry's corrupted practices and corruption of decent words to mean the opposite of their true meaning.
Words like euthanasia, compassion, shelter, humane, and welfare have all been twisted by this industry for so long and so successfully that almost no one notices that they have been brainwashed into believing the false meanings and repeating the false words like parrots.