This conflicts with reality. In the real-world where historically the cover story crashed and burned very rapidly. There was only a period of about a year after

This conflicts with reality. In the real-world where historically the cover story crashed and burned very rapidly. There was only a period of about a year after the partial recovery of K-129 before the press knew of the deception, and only strenuous efforts kept the story from being published. Even then the story was delayed only a month. In 1975 the truth of Project Azorian was public, and there wasn't widespread disbelief as you would have imagined. Nor were there men in black doing awful things to keep the story secret, just administration officials asking politely.