CMI has now published a response to the historians on their website, noting that "The historians’ description of the film, while not totally accurate at all points, is not unreasonable and in some respects complimentary." It also uses the historians' statement that had they known the nature of the film, they might not have participated, as evidence that they were justified in concealing that information from them.
CMI takes issue, however, with the two specific allegations by Bowler and Herbert that their words in the interviews were taken out of context and misrepresented in what appears in the film. To rebut them, CMI's website publishes more extensive quotations from these two historians and compares them to how they were edited and placed in the context of the film.
Although I haven't yet had an opportunity to view the screener copy of the film in my possession, the CMI rebuttal appears to be sound with respect to those two specific allegations. The CMI web page concludes by noting that each of the participants was given their raw footage, as well as a copy of the film, and ends by saying, "We are hopeful that it will turn out to have been a case of not having checked the raw footage sent to them, instead relying on memory. We would be delighted to publish news of a retraction of either or both of these two claims in this space, should that occur."
So we can add up the lessons here:
1. Do due diligence about the production company and find out who's behind it before agreeing to appear in a documentary.
2. Make sure your release gives you some way to defend yourself if misrepresented, e.g., make sure you get the raw footage.
3. If you [think you] are misrepresented and go public with it, consult the raw footage to make sure your charges of misrepresentation are themselves accurate.