I think the reason it seemed effective was the very low number of actual rabies cases. Rabies had (and still has, to a degree) a big shadow. It’s a SCARY disease, and everyone knew about it, but it was also very rare. Whenever people got bit by a dog they were probably worried, but they also probably weren’t very good at telling the difference between an aggressive dog and a rabid dog. In the article, the farmer’s neighbors “quickly concluded that the dog was probably rabid”, but I wouldn’t assume they arrived there by purely rational means.

Then look at the “rules” for the mad stone. It can’t be sold (so doctors or scientists couldn’t buy one and test it), and if you apply it to an animal it will stop working (so you can’t test it on animals). The rules keep it from being tested. Mad stones were a comfort blanket.

I don’t think this was deliberately cooked up as a way of tricking people - if so, why not charge for it? I think there were a lot of remedies that didn’t work, and the one that happened to fit the societal need of “something to comfort the large number of dog bite victims who were scared shitless that they might have rabies” (while not being easily falsifiable) survived.