Now you can't be quoting old, out-of-print books. We're talking about the OSR here, not the 1e DMG. (Which players wouldn't have had access to in any case.)This isn't true either. Those older books are full of passages about rulings over rules, not letting a rule hinder fun, etc. Are you arguing that the only PC who could be stealthy is a thief because they are the only ones with a Move Silently/hide in shadows skill? Nonsense. Every PC can attempt to hide. I don't have the 1e DMG in front of me, but I do the 2e one, and it repeats much of what was in the 1e DMG as well
So try finding that in OSE or S&W. Called out in a chart. Listed under what a character can do. Or in the examples of play. There's not even a suggestion of how to handle it other than the thief ability, which is like a 10% chance. And if a trained thief has a 10%, what can we infer a non-trained magic-user would be able to do?
Again, I'm not saying you can't do it. It's the book that's saying you can't do it. Or it just has a half-assed disclaimer to "make it up."
How to play the game isn't in the books. How to be a good GM isn't in the books. The optional rules that allowed our characters to carve out nations and reach 10th level back in the 1970s and 80s aren't there.