Mrs Palin was plucked out of relative obscurity by John McCain in the hope that her down-at-home populist style would solidify the Republican party’s conservative around his candidacy.
The incident was revealed during research for Game Change, an HBO 'docu-drama' based on a book about the 2008 campaign by two leading American journalists.
While the film is a dramatisation - with the Oscar-nominated actress Julianne Moore playing Mrs Palin - its producers conducted dozens of research interviews and Mr Schmidt confirmed its accuracy in an interview with the Los Angeles Times.
A Palin spokesman said the film - with which Mrs Palin refused to co-operate - "distorted, twisted and invented facts to create a false narrative".
The incident can be added to a long list of policy gaffes made by Mrs Palin during her three months as the Republican vice-presidential candidate.
In an infamous series of interviews with Katie Couric, the CBS News anchor, Mrs Palin was asked about her claim that Alaska's proximity to Russia gave her an insight into foreign affairs.
Her stumbling answer - describing how "[Vladimir] Putin rears his head and comes into the air space of the United States of America" - helped reinforce the impression that she was not ready for high office.
Game Change describes panicked cramming sessions during the campaign, with aides beginning their history tutorial with the Spanish Civil War and carrying through to post-9/11 era.
Mrs Palin was initially enthusiastic, making notes on hundreds of coloured flash cards, but became increasingly sullen and was described by tutors as going into a "catatonic stupor".
Although the 2008 campaign ended in defeat, Mrs Palin’s political fortunes were briefly revived in 2010 with the rise of the grassroots Tea Party movement, but is now most often seen as a pundit on the conservative Fox News cable news channel.