This catchy little phrase has no place in rational discourse and I will prove it.
Courts of law must decide upon matters of life and death and everything in between. When it comes to criminal convictions, the standard of proof is "beyond a reasonable doubt". This makes good sense - if one cannot reasonably doubt the evidence the conclusion is inescapable. Now let's take a look at a case in point regarding the "extraordinary evidence" standard of proof. We have here a diary calling into question the original authorship of certain writings. In the course of discussion, a commenter introduced evidence from the wayback machine. This evidence demonstrated the date of the original writing. The evidence was unimpeachable because (a) anyone could view it for her- or himself and (b) one cannot reasonably doubt this impartial source. Yet evidence deniers persisted in proclaiming the "extraordinary proof" standard.
With this example in mind we can now articulate what is wrong with this standard: ordinary proof is quite sufficient. Requiring "extraordinary proof" allows the rejection of perfectly good evidence. It relies upon a capricious standard existing solely in the mind of the beholder.
This is not meant as a personal attack on any individuals. I have seen this catchy little phrase all too often, by many different posters. It is long past time for it to be dead and buried. The persons citing it in the linked diary are merely the latest examples. I apologize for having to use it in order to bring this matter forth.