A promotional trailer for “The Kennedys,” a multimillion-dollar mini-series prepared for the History channel, suggests it will offer a sweeping inside look at the backrooms and bedrooms of that political clan. There are stylized re-enactments of the life of President John F. Kennedy and his family, and a title card that reads, “Behind the public image lies the story of an American dynasty.”

But concerns about the accuracy of the story presented in “The Kennedys” led to a decision by History not to show it. That decision seemed like a sudden reversal, but it came after an unsuccessful yearlong effort to bring the mini-series in line with the historical record. That effort raised questions about the boundaries between dramatic license and documented fact, a particularly fraught issue given enduring sensitivities about the Kennedy legacy.

The announcement by History in December 2009 that it was planning to show “The Kennedys” was a major step for it into scripted programming. It came at a time when History, a cable channel owned by A&E Television Networks, was shedding its reputation for musty war documentaries in favor of red-blooded reality shows like “Ax Men” and “Ice Road Truckers.” The move was meant to bring History prestige, as well as to establish a connection to the “Kennedys” producer Joel Surnow, an Emmy Award-winning co-creator of the Fox series “24” and outspoken political conservative....