Near the beginning of Foxcatcher, a solemnly moody and sometimes arresting true-life film about the destructive myth of American exceptionalism, two wrestlers begin their daily warm-up. Mark Schultz (Channing Tatum) and his older brother and coach Dave (Mark Ruffalo) are both reigning Olympic gold medallists, but their training is ritualistic and brooding, grappling moves are like aggrieved hugs and Dave suffers a bloodied nose with an air of acceptance that's as much frightening as stoic.

It would take something, or someone, outside the norm to challenge the sibling's bond, and that person turns out to be John Eleuthere du Pont (Steve Carell), the middle-aged heir to the industrial conglomerate whose factories supplied the means of American growth both economic and military. Remote and obsessive, with a bulbous nose offset by a tendency to hold his head like one of the birds he studied as an ornithologist, John builds collections, the latest of which is dedicated to champion wrestlers.

On one level Foxcatcher is a triangle of male respect and control. The taciturn and not particularly bright Mark chafes at Dave's authority and happy family life, so he transfers his allegiance to John, who in 1987 recruits him to live and train at his personal wrestling facility, Foxcatcher. John imagines himself as Mark's friend and father figure, replacing Dave, but he also needs the older Schultz's expertise and natural charisma.

Director Bennett Miller also sees this trio as symbols of America's flaws. John lives amid the revolutionary history that gave birth to the country, and his wealthy delusions include the notion that his initiatives, such as recruiting Mark and later Dave, are part of saving his country. "I'm giving America hope," John loftily declares, and there's something grotesque about his arrogance as the camera frames him against American flags and military hardware.

Miller has made three dramatic feature films – 2005's Capote, 2011's Moneyball and now Foxcatcher – and each has been based, often with liberal adaptation, on a true story. This one has the trajectory of a tragedy, and the obviousness of John's failings are part of Miller's attraction to him as a subject. His wealth has made him presumptuous: his conversations are lectures and his questions demands, but he carries on without check.

On television's The Office, Carell made deluded authority and bad judgment embarrassingly funny, and there are scenes here that are blackly humourous and cringe-inducing as well as illuminating. His wrestlers let John pin them at a celebration, while his functionaries literally hand money to his opponent at a veteran's wrestling tournament to take a dive.

In a perfect piece of casting, Vanessa Redgrave plays John's ageing matriarch, Jean, whose presence drives him to ill-judged attempts to impress her. Mother issues may seem obvious, but Redgrave gives them disapproving focus. Jean, a breeder and trainer of horses, has "world-class animals", John tells Mark, and it takes the wrestler a long time to realise that for everything John has given him - including a home, cocaine and freedom from Dave - he's really the same thing.

Channing Tatum takes Mark's self-lacerating anger to persuasive lengths and, with his thick wrestler's frame and cauliflower ears, his humanity is rendered as something blocky and unnatural (his bulky walk suggests The Lego Movie). Mark looks like something that has been made, and owned, and his rage is as inarticulate as the rest of his emotions.

The problem is that John and Mark are such troubled extremes – by the end of the film, the latter suggests paranoid schizophrenia – they can't hold up the mirror to the America that Miller envisages the film being. In Moneyball, Brad Pitt's Billy Beane was a smart, troubled man, haunted by his sporting competitiveness, but his humanity, along with his struggles, were always recognisable. That's why some of the best scenes here revolve around Dave, the most balanced of the trio and thus the one fated to be the eventual victim, as he negotiates John and Mark's strange world. It's a valuable supporting role, with Sienna Miller as Dave's wife, Nancy, little more than an onlooker. Ruffalo delivers the most telling scene, where Dave's struggle to praise John for an in-house documentary sum up his awkward position.

Bennett Miller's feel for mood – note the way John looks like he's haunting his own vast property in some shots – inflates Foxcatcher. But stripped of technique, it's a true-crime story where pulpy narration has been replaced by artful brushstrokes. It's the actors who make this movie as good as it is.