“The Beatles being so squeaky clean, they were obviously wearing the white hat,” Mr. Richards recalled. “The other role to play was putting the black hat on. The more the press played up to it, the more you found yourself thrust into the role of the villain. And then you got used to it. It was easier. You could actually be yourself in the Stones.”

That attitude not only freed the Stones to look, behave and write as they pleased, but also made them rock archetypes, living out a freedom — and license — that most fans could only wish for. Of course there had been earlier R&B and rockabilly wild men, and Mr. Jagger clearly studied them, but their careers were briefer or far less celebrated. The Stones, improper Englishmen, breached the mainstream, creating an example for every rock wastrel, talented or untalented, that followed. Decades later, on giant stages amid computer-controlled effects, the Stones’ distant whiff of anarchy is still a draw, especially because it’s underscored by the tight-but-loose sound of the band, the way even venerable songs sound up for grabs.

The Stones’ seizing of their outlaw archetype is the through line of “Crossfire Hurricane,” a documentary that hurtles through the band’s first 20 years, which comes to HBO on Nov. 15. “They start off playing this role, they become the role, and then the role nearly kills them,” said the director, Brett Morgen. Yet eventually, as Mr. Jagger says in the film, the Stones change from being “the band everybody hated to the band everybody loves.”

“Crossfire Hurricane” draws on older Stones documentaries that now look startlingly candid. Early material comes from “Charlie Is My Darling,” Peter Whitehead’s documentary of a chaotic 1965 Stones tour of Ireland that found concerts regularly cut short as audiences stormed the stage; that entire film has just been released on DVD, along with crackling live performances from the same era. The youthful Rolling Stones are earnest, thoughtful and amused by the frenzy their performances set off. “We were such nice children, underneath it all,” Mr. Jagger recalled. “It’s the blowback from Andrew Oldham: The Rolling Stones are the rebels. And the blowback was quite intense, because you got labeled with this and it was a self-fulfilling prophecy.”

Violence gave way to decadence. The Stones ended an American tour with the bleak 1969 Altamont concert in California, where four people died, and largely withdrew to studios to record two of their masterpieces: “Sticky Fingers” and “Exile on Main Street.” (The run of great albums began with “Beggars Banquet” in 1968 and “Let It Bleed” in 1969.) Cameras followed them to the “Exile” recording sessions — stoked, as Mr. Richards wrote in his book, by cocaine and heroin — and onto the road in 1972, where Robert Frank shot a rarely shown film with an unprintable title. “Crossfire Hurricane” includes uninhibited outtakes from that film, with casual nudity and open drug use. “I was a very well-adjusted” addict, Mr. Richards said. “I never felt that it hindered what I did. But it was a strange place to find yourself in and an experiment that went on far too long.”