Bridget, I'm going to take the simple route and suggest that initially it was done to save face. Had there not previously been a major cock up with an Essex case that went national? They admitted that mistakes had been made, but on a scale of 1-10, where did the marker fall?
Yes I believe there had been a previous major cock up, my memory is fuzzy, a doctor's wife maybe?
What I don't see is why it would have saved any face to frame JB rather than accept the neat and tidy package that was delivered to them in the form of Sheila.