Update: I've edited this answer to expand the material provided and to more precisely address the elements of the question, specifically, what is the factual basis for the accusation?
A quick google search for Indian attacks 1605..1776 will reveal multiple attacks. Even if we narrow the range to 1754..1776, there are attacks by Indians on colonists. Trivial Research confirms that the direct reference is to attacks on colonists in Georgia.
Did the King provoke these attacks? I think there is legitimate debate. The Colonist's claim arises from Indian attacks on the frontiers. The English crown had guaranteed those lands to the native indian inhabitants; the colonists felt that the lands were theirs. Furthermore, the colonists believed that British officials paid cash for scalps taken from colonist forces: see the following quote from wikipedia
In the American Revolutionary War, Henry Hamilton, the Lieutenant Governor and Superintendent of Indian Affairs at Fort Detroit, was known by American Patriots as the "hair-buyer general" because they believed he encouraged and paid his Native American allies to scalp American settlers. When Hamilton was captured in the war by the colonists, he was treated as a war criminal instead of a prisoner of war because of this. However, American historians have conceded that there was no positive proof that he had ever offered rewards for scalps. It is now assumed that during the American Revolution, no British officer paid for scalps.
(Although it is not relevant to OP's question, I've included the modern position that the events never happened. Scholarship on this matter has changed since I was an elementary school student, and I don't want to perpetrate myths we now doubt.)
On the gripping hand, the entire document is propaganda; it is not designed to argue facts, but to justify actions and to persuade those who were not yet committed to believe in the legitimacy of the new country. Facts and evidence are ineffectual tools for persuasion; grand claims and hyperbole are far more effective.