There has been a bonanza of sub-standard answers to this question, including baseless speculation, "jokes," and the inevitable comments complaining about deleted comments. Answers in /r/AskHistorians are expected to be comprehensive and informative. As was explained in the excellent meta post on "What it means to post a good answer in /r/AskHistorians":
If you're choosing to answer a question in /r/AskHistorians, there are three questions you should ask yourself first in turn:
Do I, personally, actually know a lot about the subject at hand?
Am I essentially certain that what I know about it is true?
Am I prepared to go into real detail about this?
Oddly enough, I can answer this one in depth with great personal knowledge... but finding decent academic sources will be a real chore for some of it.
I'll take a stab at it to start with: you'll find some reference to this in Jim Hogshire's not-that-rigorous Grossed-Out Surgeon Vomits Inside Patient!: An Insider's Look at the Supermarket Tabloids, and the subject might have did come up in Jack Vitek's The Godfather of Tabloid: Generoso Pope Jr. and the National Enquirer, one of the better historical treatments of the field. Props are also due to Paula Morton's Tabloid Valley: Supermarket News and American Culture, which is pretty darn thorough.
I am not, properly speaking, a historian, though my degrees overlap with history a little (undergrad: hermeneutics, grad: English specializing in film theory). I'm an editor, and I spent 15 years working in the tabloids.
When I was first hired as a junior writer back in the 1990s, my immediate supervisor was Joseph West. He invented the Elvis sighting in the pages of the Weekly World News during the era when its circulation reached 1,000,000. (That figure Vitek backs up, if memory serves - it's also in Morton. The importance of Joe West, though... might surface in Hogshire, and might not. Morton mentions Elvis, but I don't recall her going into any real depth.)
Oh, wait - West is sourced in Vitek! Victory is mine! (WWN fans note, the fellow being quoted there, Rafe Klinger, is the guy who invented Ed Anger.)
Anyway: a million was a respectable number for any newsweekly, and came about in part because the paper's owner and publisher, Generoso Pope, found himself in a weird situation wherein it made financial sense to print a lot of extra papers. See, he also owned the National Enquirer, and started the WWN because he had a contract with a black-and-white press, but wanted to (had to, business-wise?) put the NE out in color.
So he decided to use up his remaining black-and-white resources printing NE leftovers... stories that either weren't sensational enough for the big paper or (and this is the key part) were too hard or too expensive to fact-check properly.
Note (and Morton goes a lot into this): from this 1976 libel suit onwards, Pope made a point of hiring the best fact-checkers in the business as a form of legal insurance. He poached a few of them from Time, in the beginning.
The WWN, being a kind of experimental "why not?" project, wasn't quite as beholden to the fact-checking system, but instead stuck to lower-profile stories that were risk free (when about celebs... which became fewer and fewer as time went on) or else based on leads submitted by... the general public. And, from a libel-protection standpoint, didn't require the research the big paper did.
It started to sell better than anyone expected.
"Don't let the facts get in the way of a good story," became a motto.
Now, I'm not sure if a reader genuinely called in and said, "You know, I saw Elvis," or if the editor, Eddie Clontz, had reached the point in the evolution of the tabs when those submissions (normally dismissed by any sane newspaper) had become beside the point, and he and the reporters were free to dream up vaguely plausible submissions on their own.... As Vitek points out, there were a couple of "I saw Elvis" books out at the time that inspired the first couple of stories.
Note also: in these days, by which I mean 1977 1979 to, let's say, 1993, nearly all the writers for WWN were really reporters; they were all experienced in "real" newsgathering - West, a Scotsman, had once nearly gotten blown up while investigating a story on the IRA for one of the London papers.
So to a certain degree, the WWN culture was a kind of expression of or warped reflection of mainstream journalism just as much as, say, Hunter S. Thompson was... only in a slightly different direction. World-weary reporters given a chance to "what if" a little bit - people who knew the shape and feel of a dry investigative piece inside and out.
So. Without getting TOO anecdotal, that might start to get into some of the how and why of the persistence of the story, at least.
Edited because I'm an editor. And have a real parentheses problem, among other things.
This might be a dumb question, but is that something people actually believe? I thought it was just a kind of joke, or statement about how his influence will never die?