The so-called Waaagh!-field is a more tricky topic. I've taken a stroll through the Codex and the TT rulebooks, but could indeed not locate a specific mention of Orks making their gear work by sheer power of belief. It may indeed seem as if this is just one of the many "urban legends" within the community - personal opinion that, for whatever reason, has become so widely accepted that it is nowadays often presented as universal fact, just like with the myth about 40k canon, the oft-exaggerated body height of the Space Marines, or the Adeptus Mechanicus merely being an ally and an equal partner of the Imperium rather than a fully integrated part of it, to name just a few.
Seems I never actually read the first page of this topic.
Orks making stuff work because they believe it will, is not an urban legend, as you call it. The concept has been around since the first edition of the wargame, but with third edition the fluff explicitly said that it wasn't simply an Orc belief that various things worked better if they wanted them to. Orc weapons officially became fuelled by faith, to the extent that other races couldn't make their tech or tools work. It crept right into the rules as the explanation for why Choppas were so very good at carving up Marines, and for why a red paintjob really did make stuff go fasta as long as an Orc was driving.
If there's an urban legend here, it's that 40K Orcs aren't even more faith-powered than 40K RPG Bondage Nuns.
As for the AdMech, I'd have to go on a fluff-expedition to be certain, but I'm fairly sure it's been described as a wholly independent empire within the empire on at least a couple of occasions. I am, however, also fairly sure it's been described as something akin to a "home rule" situation pretty consistently since always. The fluff about the AdMech having a civil war ending with their formal recognition of The Corpse With No Name as their god incarnate, and them being integrated into the newly minted Imperium isn't exactly new.
... I guess my point is there's probably no such thing as 40K urban legends. It's just that the fluff can be very inconsistent, and has changed a great deal over the years.