"Extraordinary claims require extraordinary proof."
Until then, this article is probably BS.
This statement is, unfortunately, usually made to stop discussion of a proposition that the speaker disagrees with. That means the speaker believes he has some prior knowledge about the proposition that he regards as strong evidence and does not want to hear anything to the contrary. I concede that not all propositions start with maximum entropy priors. So in this case, the speaker believes he has some special knowledge about the prior probability of the truth of the proposition.
But even with such special knowledge the "extraordinary claims" language is deeply imprecise.
From a Bayesian perspective, which admits prior probabilities, even a very strong and spiked prior probability for the truth of a proposition like "nerve impulses are transmitted electrically," changes VERY quickly with contrary evidence, given even one new fact. So if, for example, there is no evidence of the heat that ought to be given off via electrical transmission, that is a very significant contrary fact and the posterior probability distribution after that fact changes the strong prior very significantly.
So "extraordinary proof" is almost a silly concept here. Of course, you want the contrary "fact" to be replicated. But once replicated, according to normal scientific standards (not double-dawg-dare extraordinary standards), that single fact changes the posterior probability profoundly.
The other evidence cited in the article, that is, the lipid solubility and it's correlation with the anesthetic properties of different molecules, is not a contrary fact--it's an alternate explanation for an observed phenomenon (nerve transmission). The existence of an alternate explanation would not change the posterior as much as a contrary fact. The existence of a viable, alternative explanation does, however shift the posterior probability.
So my point is, the "extraordinary claims" language is quite sloppy and really should play no role in scientific discussion. It's a rhetorical point to close-off inquiry, not a scientific point.
"Extraordinary claims require extraordinary proof."
Do you believe in God, Heaven and/or an afterlife?
Just askin'... ;)