I guess I don't get it, either. If you physically took your plane to a mechanic and he/she refused to provide a name and credentials, then I would agree with the hospital analogy. But this is an open internet forum -- nothing here is official, even if it comes from someone who does provide their name and certifications.
As a newbie I have found the advice here invaluable, from many sources. When I did my first oil change, I printed out a post from Roger for reference. Roger provides his credentials, but I used the information because it was well-reasoned, made sense, and I from past forum use have a positive opinion of Roger's expertise. But could I use that information in any legal capacity; i.e. logbook entry or justification of method used? Of course not.
Like most here I have also gotten plenty of good advice from "non-credentialed" posters. FredG, a few months ago you gave me some advice about flap use, which I found helpful. I used the advice despite the fact that you are anonymous and provide no credentials because it was logical and made sense and I had a good opinion of your previous posts.
I can think of several scenarios where a poster might wish to remain anonymous, for reasons unrelated to the usefulness of the information. I would hate for that person to stop posting in response.