It’s always illuminating to talk with photographers about their most celebrated pictures—especially if some of those photos have, over the years, taken on lives of their own. Example: John, Paul, George and Ringo in a swimming pool. For countless people, it’s the single most memorable photograph of the Beatles early in their career; four young, engaging, somewhat awkward English lads on the cusp of mega-stardom.

But for longtime LIFE photographer John Loengard—the man who took that picture in Miami Beach 50 years ago—the swimming-pool photo is, to put it bluntly, rather weak.

“I never thought it was a terrific photograph,” Loengard recently told LIFE.com. “It’s not a very expressive picture at all, in my opinion. But given the history and the appeal of the people in it, it keeps cropping up, year after year.”

As for how and why he took the picture in the first place, Loengard—who also served as LIFE’s picture editor from 1973 to 1987—explains that it was meant to be a cover photo, but instead ended up as a Miscellany, a popular feature that ran for years in black and white on the last page of the magazine.

“I went down to Florida to make this photo after being asked if I had any ideas on what to do with the Beatles as a cover,” Loengard recalls. “It was my idea to put them in a pool—but we couldn’t find a heated pool, the water in the pool we did use was cold, and there was always the problem of other press trying to get in. It would have to be a pool that we could close off to everyone else. So, in the end, it was a very quick shoot in a private pool, with the Beatles shivering and singing in the water before jumping out. My impression of these guys was that they were like four high school kids. You know, they had beards, sort of—like when you first start having to shave, but aren’t quite sure how to do it.

“In the end, Hedley Donovan, who was LIFE’s editor-in-chief at the time and was sitting in for the managing editor, George Hunt, decided that the Beatles weren’t serious enough to be on the cover. He ran a color picture from the war in Cyprus on the cover that week, instead.”

But Loengard does admit that he might be warming to the photo, a little bit, as the years pass.

“Recently,” he says, “after coloring the photograph myself and playing around with it on my computer, I felt—for the first time, really—that Donovan made the wrong call. It could have been a strong cover, even if it’s not a great picture.”

Not many people realize that Loengard originally shot the picture in color, but the color transparency was lost soon after the Feb. 28, 1964, issue of LIFE appeared. (At left: Loengard’s own colorized version—and cover mock-up—of the photo.)

“Harry Benson, of course, took a remarkable picture of the Beatles around the same time,” Loengard says, seemingly eager to point out a Beatles photo that he feels warrants the attention it’s received over the decades. “The one where they’re having a pillow fight in a hotel room. That is a very, very well-made photograph.”

“My own Beatles photo,” he adds, without a trace of rancor or regret, “is a second-rate, or maybe even a third-rate, picture. And yet it still has legs.”

See more of John Loengard’s work at johnloengard.com

Ben Cosgrove is the Editor of LIFE.com