I think the plot was real. Time and again, I've found that the most fantastical parts of historical fiction turn out to be the true parts, and the logic of the authors' argument for concluding that it was a real plot felt sound to me, particularly given that almost a third of the book was taken up by the bibliography!
As Mark Twain put it: Truth is stranger than fiction, but it is because Fiction is obliged to stick to possibilities; Truth isn't.”
(and before him, Byron in "Don Juan": 'Tis strange -- but true; for truth is always strange; Stranger than fiction; if it could be told...)