The CIA could not face up to the American people and admit that its former employees had conspired to assassinate the President; so from the moment Kennedy's heart stopped beating, the Agency attempted to sweep the whole conspiracy under the rug.
And they didn't have to get into a lot of legal speak or talk ER terms, they were real people. I think that's why so many actresses were attracted to it. And it was just about problems that you could identify with so much, right off the bat.