You can look at a long list of coverups/lies, that our government has since changed its story and now admits to originally covering up the first reports, long after the first coverup story. The USS Pueblo, the attack on the Maddox at Tonkin Bay, "I will not send american boys to fight in Vietnam", the U2 incident with Gary Francis Powers, the weather ballon story at Rosswell, "I did not have sex with that woman", "read my lips", etc. etc.
A governments credibily is built up over time, and trust is earned.