Ms. Palin attempts to paint a picture of Revere as a provocateur, waving the proverbial red flag in front of a bull to get it to charge, warning the British not to mess with the colonies. However, Revere's own hand betrays Palin's inaccuracies: In a letter written about his famous ride, Revere describes himself and his company (Revere was not alone in his efforts) as taking extreme pains to make sure that the British were as ignorant as possible about American movements.
In fact, the only "warning" that Revere gave to the British was when he was detained briefly by the British, and that information was only surrendered when a British officer held a gun to his head and threatened to blow his brains out. While the idea of Revere racing through the street calling out "The British are coming!" has a certain romance to it, it's utterly false: Revere took great pains to select only trustworthy Patriots to spread the word door-to-door in a concerted effort to prevent the British from finding out American plans.
Ms. Palin's view no doubt holds a certain romance to a segment of American society, but it's wrong, and you have that from Paul Revere himself.