You needn’t accept the most scabrous speculations about John Lennon’s life to wonder if this depiction isn’t seriously oversimplified and a bit glorifying.

As its title promises, Leaf and Scheinfeld’s tautly assembled documentary is primarily about the Nixon administration’s attempt to have the most troublesome Beatle deported from this country. The movie doesn’t attempt to be a complete account of Lennon’s life in the states, which is entirely reasonable. But there are many holes in the story, and most of them flatter the martyred Lennon and his widow, who has maintained rigorous control over his legacy.

The film opens with the “Free John Sinclair” rally at which John and Yoko appeared, and a flurry of comments by such zeitgeist authorities as Gore Vidal and G. Gordon Liddy. Then it backs up to the controversy over Lennon’s comment that the Fabs were “more popular than Jesus,” only to start moving forward again, through “All You Need Is Love,” the escalating war in Vietnam, John meeting Yoko, the Black Panthers, the 1968 Democratic Convention, “Revolution,” the couple’s “bed-ins,” “Give Peace a Chance,” Nixon’s “plan to end the war,” the invasion of Cambodia, and so on. If any of those references seem cryptic, The U.S. Vs. John Lennon will be edifying. For people who remember the period, however, the film doesn’t add much.

Somewhere in all this, John and Yoko relocated to New York and suggested that they might play a 1972 anti-Nixon tour. Sen. Strom Thurmond was alarmed, and soon Lennon’s visa was at risk, which was legally justifiable since he’d pleaded guilty to marijuana possession in Britain. Lennon claimed he’d been framed, but the Beatles’ use of drugs was no secret. That’s not something this film says out loud, though. There’s a snippet of “Cold Turkey” but no acknowledgment that the song was inspired by Lennon’s heroin addiction.

Other pieces of the tale slip by, intelligible only to people who already know the history. There’s a shot of the famed couple with Kyoko, Yoko’s daughter from her first marriage, but there’s no mention of the fact that the 1971 move to New York was partly spurred by Yoko’s hopes (ultimately dashed) of getting custody. And somehow it goes unnoted that John and Yoko were splitsville for part of the visa-battle period.

The film’s most telling deficiency, however, is not in information but in analysis. Lennon was a powerful youth-culture symbol and a man with natural anti-establishment sympathies. Yet his “radical” period was brief and ambiguous. (Which version of “Revolution” do you think expresses the real John? Sorry, you’re both wrong.) This documentary hints that the musician withdrew from the anti-Nixon tour because of concerns about his visa, thus proving that the White House was diabolically effective. But it’s just as likely that Lennon simply lost interest, especially after his one pro-revolution album, 1972’s Some Time in New York City, flopped both critically and commercially.

Of all the film’s pundits, who range from George McGovern and Ron Kovic to Noam Chomsky and Geraldo Rivera, only Liddy seems to discount Lennon’s supposed threat to Nixon. Yet the evidence strongly suggests that John and Yoko were dilettantes—or, if you prefer, conceptual artists. The U.S. Vs. John Lennon prefers the good-triumphs-over-evil narrative that cuts from Nixon’s resignation to Lennon’s getting his green card. But a more amusing, and probably truer, version of the story would show Nixon battling to deport a fickle rocker who’d already forgotten that he’d ever written a dumb ditty for John Sinclair.