On March 10, 2008, The New York Times revealed that New York Gov. Eliot Spitzer was a regular client of an escort service called the Emperor’s Club. After a blitz of mass-media coverage, Spitzer promptly resigned, shamed and ridiculed. But the new documentary “Client 9: The Rise and Fall of Eliot Spitzer” asserts that there was more to the story than sex. Plunging us into an ocean of grudges, rivalries and misdeeds, Oscar-winning documentarian Alex Gibney reveals the hidden conflicts that turned Spitzer’s fall into a fall in flames.

“Client 9” follows Spitzer’s meteoric rise, starting with his extremely productive years as New York State attorney general. His bold tactics consistently produced the results he wanted. However, his tough talk and harsh prosecutions also made a distressing number of powerful enemies — Ken Langone of Bank of America, Hank Greenberg of AIG and John Whitehead of Goldman Sachs — just to name a few. When he was elected governor, he made another enemy in Joe Bruno, the Republican majority leader of the state Senate.

Gibney makes a convincing case that these influential figures all came to bear a personal grudge against Spitzer, and when he presented them with that golden opportunity, they struck. Speeding along the investigation into his activities, leaking classified investigation findings to the press and hiring PR firms and private eyes to ensure that the story would be as widely seen as possible, Spitzer’s nemeses used their influence to make sure that his fall was as public and painful as possible.

It would have been all-too-easy for Gibney to make this a simple tale of corporate abuse of power, presenting Spitzer’s enemies only in villainous-looking photographs. But he is too smart and too canny a storyteller to simply trade one dogmatic narrative for another. He gives Spitzer’s enemies copious amounts of screentime (in which, it must be said, they seem to have little interest in challenging the film’s allegations), along with lengthy interviews featuring Spitzer himself.

Gibney has made this kind of documentary his speciality. His “Enron: The Smartest Guys In The Room” made the case that Enron’s fall secretly began even as the company was rising, while his Oscar-winning “Taxi to the Dark Side” revealed strong evidence of CIA misconduct in Afghanistan. In both films he presented a familiar and well-publicized story with a new twist. He does the same thing here, complicating a story that we think we all know and drawing a fascinating tale from the feuds, insults, infidelities and imperfections.

Spitzer made a stupid mistake, to be sure. He will be the first to admit this, saying firmly, “I brought myself down.” But what makes “Client 9: The Rise and Fall of Eliot Spitzer” so worthwhile is that it consistently refuses to draw any easy lessons from this unholy mess. This is a story about human passions and frailties, and there are few teachable moments.