Imagine if a U.S. president were to flagrantly make up a claim that some other country was developing weapons of mass destruction. Imagine that there was no way to verify this claim. Imagine that the president insisted on invading said country on the basis of the unsupported claim.
Do most people still expect that someone in that position will not post clearly false messages, specially when those messages affect something as fundamental as the death of thousands of people and the overthrow of a government?
Iran contra, Watergate, Vietnam, ...
Is there any trust left?
It's bewildering that the answer is, "Yes". It's discouraging that so many presidents have so often deceived the people so horribly. It's much much more discouraging that the people don't learn.