Didn't any of all these experts and scholars they interviewed point out the rather glaring errors?
Bearing in mind that I haven't seen this particular one, but: My admittedly fuzzy idea of how such things are produced indicates that they probably have a LOT more interview footage than wound up in the show. It's entirely possible that one or more of the experts interviewed did give information that would have contradicted what History Channel was presenting. Ultimately, though, their goal is ratings, which means entertainment--not necessarily good scholarship.
I am not accusing them of deliberately editing to tell the story they felt would sell best, by any means. I have no proof of that even if I wanted to make such an accusation, and it would be unwise for me to do so based on secondhand information. What I'm saying, though, is that it pays to keep in mind that their goals are different from someone writing an academic paper, and that the difference of focus *might* affect their choices about how the material is presented.