Source, the Smithsonian. I do not know if you could classify it a conspiracy. More of a cover-up.
According to the documentation at the Smithsonian, the government feared the public repercussions of the Sabre breaking the sound barrier, as the public was told the money needed for the X-1 project was all about the race to break the sound barrier.
Go to the Smithsonian, read all about it. A subtext of the docs was printed in Air & Space as well. How can you guys be plane fanatics and not get Air & Space?