1. One of my favorites is "George Washington could not tell a lie"
The story of Washington and the cherry tree originated in an early 19th century biography by Mason Locke Weems, generally known as Parson Weems. There is a lovely painting by Grant Wood,
As far as not lying, when Washington was offered the post of Commander-in-Chief of the Continental Army, he was also offered an annual salary of $10,000. He replied that if Congress would just pay his expenses, he would not take a salary. Congress took him up on it. Well, they came to regret it, as his expense accounts came to well over $10K per year. His reported laundry bills in particular seem to be exercises in fiction.
When Washington became President, he said that he would not take a salary if Congress would pay his expenses. Congress told him that he was getting a salary.
"In a well-ordered republic it should never be necessary to resort to extra-constitutional measures" -- Machiavelli, Discourses on Livy