In my opinion, they are. On the one hand they want ONLY ultra-compassionate people who have feelings for the animals to perform "euthanasia", but on the other hand they expect these same people to have the mental toughness to kill large numbers of animals. I don't believe you can have both criteria within the same person, because they are a paradox by definition and anyone who TRULY meets the first set of criteria could not be capable of meeting the second.
And therein lies the problem with Humane organizations running pounds.