The Guardian doesn’t have the nickname “The Grauniad” for nothing, a paper likely to spell its own masthead wrong.
The nickname Grauniad was reportedly coined by the British satirical magazine Private Eye. This seems to be confirmed by the following, from The Economist (London) of 27th November 1971:
All the characters of Private Eye’s earliest days survive—Lord Gnome, the Grauniad, Lunchtime O’Booze—giving a curious cosy familiarity to each issue.
The world needs more “those guys”, especially when they actually know what they’re talking about.
I was only quoting the explanation, but as far as I can tell, part of the joke is that the paper was so regularly riddled with typesetting and spelling errors that The Guardian could make an error with an unchanging block that should be almost impossible to get wrong without deliberate effort.
As to whether they meant the nameplate or the masthead, this is a distinction I’d never heard about before, so I’ve learnt something there!