Wiktionary
n. A discrepancy between the statements made by a person in authority (especially by a politician) and the perceived truth
Wikipedia
Credibility gap is a term that came into wide use with journalism, political and public discourse in the United States during the 1960s and 1970s. At the time, it was most frequently used to describe public skepticism about the Lyndon B. Johnson administration's statements and policies on the Vietnam War. It was used in journalism as a euphemism for recognized lies told to the public by politicians. Today, it is used more generally to describe almost any "gap" between the alleged reality of a situation and what politicians and government agencies say about it.
Usage examples of "credibility gap".
During his university years, it had been a running joke among fellow arts students, regarding the credibility gap between their encouraged ambitions and their realistic future employment prospects.
Soon, a new credibility gap will emerge as the Pentagon attempts to massage the news.
Trismegistos, drummer with the Credibility Gap, watched placidly from only a few feet away, seeing them as a very complicated, almost mathematical ballet.
M: So, my suggestion to you on compiling our E-mails is to be cautious in the presentation, because there is, from the feedback represented by a very limited sample observed, a huge credibility gap between something written at the 6th to 8th grade level, and that of the more scholarly level.