But, but... we were always told that Franklin was an expert crystallographer and that Watson and Crick were bumbling amateurs who knew nothing, NOTHING, about crystallography!
Franklin was. Which is why she was the one who actually produced that image. And if the problem could have been solved by deducing the crystalline structure from variant A, she would have been a much better choice.
The fact that Crick was the world expert on the one obscure thing about crystallography that mattered here doesn't mean that Franklin wasn't the real expert. Every expert has gaps in their knowledge.
Using Fourier transforms doesn't seem obscure to me. It seems to me -- today -- that it is an obvious thing to do. It probably was back then, too, if you were a physicist who was good at math.
The fact that Crick was the world expert on the one obscure thing about crystallography that mattered here doesn't mean that Franklin wasn't the real expert. Every expert has gaps in their knowledge.