1) The frequency order of letters in English is ETAOINSHRDLU...
2) As a result (for physical reasons, which would take longer to explain), the arrangement of the keys on Linotype typesetting machines was not QUERTY, but frequency arranged columns: ETAOIN was the first column (reading downward), SHRDLU the second, etc.
3) The Linotype (which produced slugs of hot type metal from brass molds) did not have a backspace. It was a complicated process to get rid of a mistyped line.
4) So when they made a mistake, lazy linotypists would fill the rest of the line with garbage, so it would get pulled later by the proofreaders (lines of type were metal objects).
5) What is the easiest way to fill a line with random characters? (exercise left to the reader).
6) Not all proofreaders are alert. Therefore lines full of things like SHRDLUSHRDLUSHRDLU occasionally found their way into print (I have a collection of odd clippings that people sent me over the years -- they have long since stopped coming, as computer typesetting replaced the Linotype).
7) MAD Magazine authors picked up these sequences as nonsense words and used them as you mention above.
8) I read MAD in my youth.
9) When it came time to name the system, I tried to come up with acronyms and none were very good so I decided to just pick something that looked like an acronym but wasn't. I reached into my memories for a random sequence.
10) Several years later, someone gave me a copy of the science fiction story by Frederic Brown, written originally in 1942(!), entitled "ETAOIN SHRDLU" in which an artificially intelligent Linotype machine (with natural language ability) learns everything it typesets and tries to take over the world (World of Wonder ed. Fletcher Pratt (New York: Twayne, 1951, $3.95, 445pp, hc)). When I saw it, it seemed vaguely familiar, so I suspect that I had read it during my science-fiction years in high school, and it had stuck somewhere in the dim recesses of my memory and popped back out when appropriate.
p.s., the hero outwits ETAOIN SHRDLU by having it typeset every book on Buddhism. The story ends: "See, George, it believes what it sets. So I fed it a religion that convinced it of the utter futility of all effort and action and the desirability of nothingness...It doesn't care what happens to it and it doesn't even know we're here. It's archived Nirvana, and it's sitting there contemplating its cam stud."