Personal opinion. The 1e, 2e, 3e DMGs do not do a good job of cluing in a DM on what a DM is going to do a lot of (which is adjudicate situations, from the mundane to the completely gonzo off the wall ideas players will come up with)
Gary Gygax writes in 1E about it, but it is on page 110. You had to read 109 pages before you got this bit of wisdom (Image 1)
David "Zeb" Cook might have written about it in 2E. There is some hint of it on page 38 (first print) but it deals with the optional non-weapon proficiences. (Image 2)
Not sure who wrote the 3E verbiage (Image 3), but it really hits the wrong tone for how I like to think about running the game. But at least it is on page 9.
In my opinion, adjudicating should be the 1st or 2nd thing the DMG goes over. And the DMG should provide copious amounts of advice on how hard the job is, and throw in some easy to use modifiers and ideas about how to mechanically adjudicate things.
I think STAR FRONTIERS released in 1980 does a much better job of giving a simple to understand mechanic that can be used to adjudicate most situations. (Image 4).