#mostly because of

First, what Norman claims happened.

The fact that Little Richard was in Europe wasn't extraordinary to begin with. A lot of his following back in America had fallen off as a result of his brief stint in religiosity, but his popularity in Europe hadn't yet waned. As a result, it was easy enough for Brian to arrange for a single performance by Richard helmed by NEMS Enterprises, which would take place on 12 October 1962. Also performing that night were the Beatles.

Per Norman, "Putting them on the same stage as one of their greatest musical heroes ended what they'd viewed as Brian's probationary period." That he'd been able to wrangle such talent as Little Richard seemed proof enough for them of Brian's adequacy. Ten days prior to the performance, "they signed a second management contract to replace the one that had included Pete Best... raising [Brian's] commission to 25 percent," a fact which was undoubtedly sweetened by the Beatles' subsequent meeting with their childhood hero.

When Little Richard arrived in Liverpool, so too did the tour's promoter, Don Arden. Apparently Brian and Arden got into a dispute before the show, which ended with Brian saying, "I'm going to telephone your office tomorrow, Mr. Arden, and after that I don't think you'll be working there anymore." Also not helping matters were the "horror stories of [Little Richard's] unreliability, his bizarre whims and fancies, his frequent refusal as an ordained minister to sing anything but hymns, and his paradoxical fondness for onstage stripteases, ignoring the audience's pleas for 'Good Golly Miss Molly' or 'Lucille.'" Clearly Brian had his work cut out for him. But as Norman somewhat wistfully notes, "That night in New Brighton, he ululated every one of his Golden Oldies with scarcely a pause."

The reasoning for this turn around was simple: as Joe Flannery recalled, "Brian seemed to be able to do anything with him. When he finished his act, something went wrong with the mic for the next act, Pete MacLaine and the Dakotas. Brian could even get [Little Richard] to walk across [the stage], nice as you please, and hand his personal microphone to Pete MacLaine."

A second Little Richard performance in Liverpool—also featuring the Beatles—took place only two weeks later, an astonishment to many, though "Joe Flannery claimed to know the reason for this seemingly inexhaustible willingness to oblige Brian and make the Beatles look good. 'Richard was gay... or, to be precise, he was everything... and he and Brian had spent the night before the Tower Ballroom show in a suite at the Adelphi Hotel.'"

Fortunately for us, despite both parties' (understandable) radio silence on the matter, Philip Norman got to investigate this matter for himself. Years later he met a "terrified" Little Richard aboard a flight with whom he felt "bonded" due to their "mutual terror" of flying.

"When the plane leveled out and his prayers subsided, I said, 'May I ask you something?' "'Sure,' he replied. 'Anything you want.' "'On 2 October 1962 [sic], when you appeared with the Beatles at the New Brighton Tower Ballroom, had you spent the previous night with Brian Epstein at the Adelphi Hotel in Liverpool?' "I think I may have been the only person ever to reduce Little Richard to silence. Then he broke into denials almost as passionate as his prayers: 'No! No! No! No! I never even had a sandwich with Brian.' "Knowing that, in certain circles, 'sandwich' can mean something far from Prêt à Manger [oral sex, whose usage dates as far back as Oscar Wilde and Bosie Douglas], I didn't press the point... but I still wonder."—Mr. Moonlight by Philip Norman

So that's what Norman says occurred. But what of other biographers?

The Man Who Made the Beatles by Ray Coleman makes no mention of Little Richard whatsoever. There don't seem to be any online copies of it available, so I can't check the more thorough In My Life by Debbie Geller. As far as periodicals and newspaper coverage go, the only other times Brian and Little Richard ever had their names associated was in 1966 when Little Richard was one of the many American acts performing at Brian's Saville Theatre—a move which, at the very least, points to the longevity of their working friendship.

The only other tidbits I could find on them are few and far between, and don't point to any spectacular one night stand. From The Beatles' Every Little Thing by Maxwell Mackenzie: "Little Richard said that Brian Epstein offered him fifty percent of the management contract if he could get the Beatles an American studio. He refused, not wanting to get into the management business and thinking that the band would never make it." I kind of take this with a grain of salt due to a quote Little Richard gave to Mersey Beat right after sharing the stage with the Beatles where he said "Man, those Beatles are fabulous. If I hadn't seen them I'd never have dreamed they were white. They have a real authentic Negro sound," which is a bit of an aside here but I thought was quite interesting. Anyways, Richard was known to flip flop on his beliefs, so maybe this is another instance of that, but I don't know.

Similarly, both George and John mention the 12 October performance in the Anthology book, but there's no mention of anything between Brian and Little Richard beyond Brian having set up the event.

So to make a long story short, I honestly have no idea where Norman got the idea that this is some longstanding rumor we've all been dying to see confirmed or denied? Everywhere else I look, I cannot find a single corroboration of anything Brian/Little Richard related, whether it be sexual or professional in nature (the latter being Brian's supposed "extraordinary" talent in managing Little Richard compared to others). I can't find any other place where Flannery has made these claims either. Granted, Flannery was in a romantic and occasionally sexual relationship with Brian at this point, so maybe—probably—he was privy to more information than others, but you never know. I mean, the guy didn't even bring it up in his own memoir.