Is this accusation in the Declaration of Independence factual?

This is not actually an answer to the question as stated, but rather a commentary on "them criticizing the founders' attitudes regarding the American Indians" (which does seem to be the actual crux of your question, however).

It should be noted that Thomas Jefferson (also, obviously, the principal author of the declaration of independence and therefore the statement in question) had the following to say in his first State-of-the-Union address:

Among our Indian neighbors also a spirit of peace and friendship generally prevails, and I am happy to inform you that the continued efforts to introduce among them the implements and the practice of husbandry and the household arts have not been without success; that they are becoming more and more sensible of the superiority of this dependence for clothing and subsistence over the precarious resources of hunting and fishing, and already we are able to announce that instead of that constant diminution of their numbers produced by their wars and their wants, some of them begin to experience an increase of population. (Source)

It should be clear from this that the founders of the US did not intrinsically hold any bad attitudes towards the Indians, but rather had an interest in seeing them flourish and wanted to engage in intercourse with them.

As for what explains the apparent discrepancy between this statement and that in the declaration of independence, I cannot say for sure, of course, but if I were to speculate, I would choose between the following explanations:

• "The merciless Indian Savages" was not meant to refer to all Indians as a whole, but rather specifically to those who were incited to attack the colonists.
• They were (perhaps righteously) infuriated at the Indians at the time of the writing of the declaration of independence and lashed out at them in anger.
• They wanted to portray the Indians as universally merciless savages in order to gain the sympathies of the Old World to which the declaration of independence was, after all, addressed.
• Perhaps their views on the Indians changed in a few decades.

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.[20] It is now assumed that during the American Revolution, no British officer paid for scalps.[21]

(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.

The quoted indictment, the 27th against the King of England, refers to the use of slaves and Indians against the colonial rebellion. The most notorious of these policies was the Dunmore Proclamation (1775) which offered freedom and weapons to any slave in Virginia that would fight against rebellious colonists. The Virginians were infuriated by this act. The "Savages" charge arose from the Proclamation of 1763 which declared all the land beyond the Appalachians as belonging to the Indians. The withdrawal of British support for frontier colonialists resulted in many massacres of families who had ventured into these areas. The Virginians were particularly offended by this proclamation, because many of the settlers of the Youghiogheny River Valley who were getting slaughtered were from Virginia. It was also well known that British officers were cosying up to different Indian tribes, especially the Mohawks, and making non-aggression pacts with them. These agreements gave the Indians free hand to attack wayward settlers who strayed too far west.

To my knowledge the British did not specifically sponsor any Indian raids or provide them with free weapons before 1776. In general, the British policy was to maintain neutrality with the tribes.

I doubt the quoted indictment is about the Royal Proclamation of 1763 (that forbade settlement beyond the Appalachian Mountains). I think the quotation refers to the contemporary state of affairs months or even just weeks before the drafting of the Declaration of Independence in June 1776.

In March 1776, there were widespread rumors about Sir John Johnson "boasting about calling the Indians to attack the rebels". In this case, as in the majority of others, the Indians remained firmly neutral.

One solid example to back up the Congress's indictment was John Butler of Niagara who recruited about 100 young warriors (mostly Seneca Indians) against rebels. The warriors' action was, however, against the wishes of their chiefs (see Nester 2004).

In fact both rebels and loyalists actively tried to incite Indians against one another (see Dunn).

I think that the said indictment expressed rather the fears of the Continental Congress than the known facts. Their intuition was that rebel English colonists would be always the last that Indians would ally with. The colonists, no one else, had been directly responsible for taking more and more Indian land in the past and provoking the conflict. All parties, rebels, Indians and loyalists, knew that white colonization wasn't favored by the King of England; it was fueled by colonial elites, the same people that later became the core of Colonial Congress.

Congress's intuition about Indians had proven true during the War on Independence, when Indians either joined the British or stayed neutral.