
I know that the reptile vet that I go to uses freezing for euthanasia. I am afraid that I would want to see more credentials from the article writer before I believed her over my vet and his description of how the freezing process slows down cold-blooded animals.
Speaking of reptiles, I have to point out another method of euthanasia: predators. Not always available, probably not very humane, but natural.
The natural history museum method is to just drop the critter in alcohol for preservation, but I'm not a fan of that.
And then this is just my two cents -
The goal of euthanasia (in my opinion) is to stop an animal's suffering, so if I make the descision to euthanize, the animal is already obviously in pain. (Unlike some of the references, where researchers are putting down animals who are healthy, and thus risk creating pain where there is none.)
Putting it in the freezer, it has a few more hours of pain ahead of it; leaving it in a shallow bowl, it has days. Of those two options, freezer wins.

The reason that freezing is good for aquarists is simply that you cannot mess it up. Someone who tried to pith a frog without being confident in what they were doing would just give the animal a gruesome and drawn-out end. Someone who didn't mix strong enough chemicals would also end up torturing a critter to death, perhaps over a period of hours. Recommending freezing to aquarists as a means of euthanasia is largely to protect the dying animals from owners in my opinion. If a new method is devised it must be foolproofed before being promoted.