I think where SirStevO and BladeVenom are at loggerheads is the fact that you're technically arguing about two different things:
SirStevO is arguing that the act of euthanizing stray companion animals is humane and "ethical" when taken at face value
BladeVenom (and many other posters ITT) is arguing that the act of euthanizing stray companion animals is hypocritical in light of PETAs broader definition of "ethics" concerning all animals
I agree with SirStevO that compassionate euthanasia is quite often the "ethical" option. I also agree with BladeVenom that PETAs working definition of "ethical treatment" of animals (all animals are on par with humans, killing animals is murder, using animal products should be combatted with violence, etc) does not reconcile with the preceding sentence.
While I might question the motives behind the source in the OP that is not enough to broadly discount the allegations. And those allegations are pretty ugly. If PETA does indeed euthanize 84% of companion animals within 24 hours of arrival that would seem to be a figure grossly disproportionate to other, similar organizations like SPCA. Indeed, around here an organization euthanizing 84% would be labeled a "high-kill" shelter and other rescue operations exist to take animals off the hands of shelters whose prevailing solution seems to be euthanisia.