Various comments made elsewhere include:
In other words, the standards for what is authoritative clearly depend on the claim being supported. (Link)
We require references to be of a certain reliability, from a source who has a certain authority on the matter at hand. (Link)
I'm not a fan of the "authority" phrase - I couldn't define what it meant without tripping over "Appeal to authority" fallacies. (Link)
Also, the famous answer about torture doesn't cite any methodologies (instead its references are all "appeals to authority") ... is it a bad answer then? (Link)
The latest example I've seen is in this answer about dolphins ...
In the presence of a shark, dolphin anti-predator behavior varies with the circumstances. Some simply swim away from the shark, others ram or bite it, and yet others launch coordinated group attacks to drive the predators away. -- Smithsonian National Zoo
... which looks like it's relevant but which is unverifiable.
So: how does an unverifiable allegation published by the Smithsonian (for example) compare with an unverifiable allegation published by a member of the forum?
To take another example, Dian Fossey is considered an 'authority' on the subject of gorillas. Part of her knowledge was from first-hand experience, i.e. field observations: camping in the bush, having a look, and journalling her observations. Why makes 'scientific' observations more authoritative than mere 'anecdotes'?