From Thomas Kelley, Inspector of Secret Service, Interrogation Report on Lee Oswald.
I approached Oswald then and, out of the hearing of the others except perhaps one Captain Fritz's men, said that as a Secret Service agent, we are anxious to talk with him as soon as he had secured counsel; that we were responsible for the safety of the President; that the Dallas Police had charged him with the assassination of the President but that he had denied it; we were therefore very anxious to talk to him to make certain that the correct story was developing as it related to the assassination.
He wanted to make sure the correct story was developing, in the face of Oswald's denials.
The wording says it all. He doesn't say we want to make sure the police have their facts straight - no. Facts are adduced from the evidence and are merely the building blocks of "the story".
The story is everything, because it incorporates means, opportunity and motive. To create a patsy, you have to start with a rudimentary story and try and fit whatever evidence you can around it, pad it out with created evidence and suborned testimony, and be prepared to be flexible insofar as you may have to change parts of the story here and there for any number of reasons. If you do need to change parts of the story, you simply continue on as if that had been the story all along.
But the real jewel in the crown is the confession. Wringing out a confession means you don't need much else. A lot easier all round.
Oswald might have survived a while longer if he had confessed. False confessions are common.
Kelley knew about the creation of stories. The Secret Service also learned the Reid Technique. Reading this part of his report, you could almost get the impression Kelley was guessing that the cart (the story) was being put before the horse (the evidence carrying the facts).
If that is what he thought, he was right.