credibility gap

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun Public skepticism about the truth of statements, especially official claims and pronouncements.
• noun Lack of trustworthiness.
• noun A discrepancy or disparity, especially between words and actions.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A discrepancy between the statements made by a person in authority (especially by a politician) and the perceived truth