The public is always told the truth. Political leaders never lie. That also goes for cops and lawyers
Of course people lie, everyone on the Planet has told a lie, but more importantly people also talk and as Benjamin Franklin once said "Three May Keep a Secret if Two are Dead" and on a case of this size there are hundreds perhaps thousands of potential leaks but the CT's want us to believe that all these people even after decades had their mouths permanently glued shut and as we know that assumption just isn't Human nature.
Every big secret eventually comes out, because people blab, it's a fact of life.
JohnM