It should probably surprise no one that a new documentary about “the quiet” Rolling Stone, Bill Wyman, has kicked up a controversy over what it doesn’t say rather than what it does. Last month, a planned showing of the Oliver Murray-directed film The Quiet One at the Sheffield Doc/Fest drew outrage, and was cancelled, due to what was seen as its insufficient probing of Wyman’s 1989 marriage to Mandy Smith, who was 18 at the time, but whom he began allegedly grooming when she was five years younger than that. (At that time, he was 47). Back then, the story raised some eyebrows in the US, and inspired reams of harrumphing coverage in the British tabloids, but not quite the censorious outrage it might have received today.

In fact, the documentary, which is being shown as part of this year’s Tribeca film festival, does allude to part of the controversy. Fleetingly, Wyman defends his relationship with Smith by saying “it was from the heart. It wasn’t lust, which people were seeing it as.” Notably, he does not talk about how old she was when they first had sex. Of the marriage – which resulted in a separation three years later, and a divorce two years after that – he says, “I was really stupid to ever think it could possibly work. She was too young. I felt she had to go out and see life for a bit.”

In Wyman’s 1991 autobiography, A Stone Alone, he was more forthcoming. “She was a woman at 13,” he wrote. “Everyone accepted her as an adult without question.”

The film is even more circumspect about the most improbable aspect of this story. There’s no mention that, in 1993 – the same year Wyman divorced Smith – his 30-year-old son Stephen married Smith’s mother, who was then 46. (That couple split two years later.)

Such oversights demonstrate the depth of the director’s deference to his subject. But, in return, it would have been nice if he got meatier, or rarer, material from Wyman regarding what the film’s potential audience cares about most – the story of the Stones. Other than one extraordinary scene at the movie’s end, and a few choice bits along the way, The Quiet One skims the surface of the band’s history, alighting mainly on the dramatic highlights – the early riots the band inspired, their contrary image in the press, the 60s drug bust, Altamont. There’s real reason to have expected more fresh material given Wyman’s well-known role as the Stones’ most dedicated, and informed, archivist. He has filmed, saved or collected more about the band than anyone else on Earth. The film positions this fact as a central part of Wyman’s character and even features many scenes of him in his archive where, puzzlingly, he’s shot from behind and in voiceover rather than while speaking directly to the camera.

Perhaps that set-up is meant to underscore the enigmatic nature of his character, something the film provides ample evidence of. Newspaper clippings amplify his reputation as “stone face” based on his affect, which is so deadpan, it could make a corpse look like the life of the party. Wyman also tends to stand stick-stiff on-stage, holding his bass like a soldier with his weapon at rest. In terms of his instrument, there’s a brief allusion to how Wyman wound up inadvertently creating the world’s first fretless bass, an important enough innovation to have merited more discussion.

Bill Wyman and Mandy Smith in 1989. Photograph: Peter Brooker/ Rex Features/Five TV

There is, however, some nice testimony about his unfussy, but highly effective, approach to the bass from informed observers like Eric Clapton and the producer Glyn Johns. He modeled his work on that of Donald “Duck” Dunn of Booker T and the MGs. Clapton calls Wyman’s bass lines “fantastic, unique. It was so precise and so contained. It was just right,” he says.

“Leave space, don’t fill it up,” Wyman says of his approach. “You’re not a fucking lead guitarist. Focus on the drums, so you’ve got a solid foundation that everyone can draw upon.”

The film features some telling quotes from the star about his frightening childhood in the 1940s, when German bombs rained down on his London neighborhood, killing classmates. There’s also important stuff about his relationship with his family. His parents had a “children should be seen and not heard” approach to rearing. Wyman says his father hated his son’s ambition to rise above the family’s poor status, viewing it as a betrayal. Though Wyman says he later forgave his father, scars seem to remain. There’s choice footage, too, of the early days of the band, though, like his childhood years, it’s sometimes padded with stock footage or, when all else fails, animation. As they progressed, Wyman stood apart from the other Stones through his lack of interest in drugs. Instead, he admits, he “probably had an addiction to sex”.

That addiction merits about two sentences in the film. In Stone Alone, the bassist was more effusive on the subject, while also tipping off his talent for chronicling. “I fared much better than the others in the girl department,” he wrote. “In 1965, we sat down one evening in a hotel and worked that out. Since the band had started two years earlier, I’d had 278 girls, Brian (Jones) 130, Mick (Jagger) about thirty, Keith (Richards) six, and Charlie (Watts) none.”

More detail of this sort would have been a useful addition for the film. Many of the subject’s observations are bland. He describes the Stone’s historic concert in Hyde Park, directly after the death of Brian Jones, simply as “extraordinary”.

He’s more colorful about the Stones’ time as tax exiles living in France, where he met James Baldwin, who introduced him to the music of Ray Charles, who became his idol. There’s also rare footage of Wyman creating his hilarious, new wave novelty, solo hit in 1981, Je Suis Un Rock Star, as well as of his heady time backing Howlin’ Wolf, along with Clapton and Charlie Watts.

Of his dramatic decision to leave the Stones, after the 1990 Steel Wheels tour, he says, “I loved what we achieved. But I needed to sort out my personal life – and my future.”

Observers say he has used his time well since then, becoming more appreciative of life and more connected to others. That’s evidenced by a seemingly strong relationship with his third wife, Suzanne Acosta, whom he married in 1993 and with whom he has three children. In the last part of the film, Acosta appears with him in the only scene where he speaks directly to the camera. What follows is as beautifully honest as much of the rest is vague. Wyman tells a story about meeting Ray Charles with such passion, he has to halt several times to keep the tears from flowing. What he finally describes of that meeting offers the first true insight into the hurt, and insecurity, that lies behind the cool front he put up with the Stones and in much of the film. Still, it’s left to his current wife to provide insight into his seminal need for collecting. That desire, she says, reflects a “need to relive his life and find out who he was”.

From the evidence here, it seems that need remains unfulfilled. “It’s bizarre,” Wyman says at the end of the film. “It’s a bizarre life I’ve had.”