Call me flippent if you like, but if the Hapsburgs and Bourbons were illegally usurped then, gulp, are not the United States of America still the rightful property of the British Crown?
However, even assuming the war of 1776 was a war of independence not a "revolution" (the the colonists never sought to overthrown the government of Great Britian, only to free themselves from it's influence). The Louisana purchase is in my mind invalid having been negotiated with an illegal, revolutionary government of France, the Western US is the legal property of HM Juan Carlos of Spain and Hawaii is an occupied foreign nation.
This is all rather irrelevant tho, revolutionary government do not respect the laws of property.
While I would have supported the Loyalist cause (as all good New Jerseyans did, including our governor William Franklin), the Treaty of Paris did legally grant independence to the colonies. It's ironic, but accurate, to claim that the legitimacy of the United States was guaranteed by the King of England.
If there is any usurping that was done, it was in the triumph of Lincoln's central government over the Confederates States. Thereafter, the federal government has been like a black hole, absorbing our rights one after another.
As has already been explained above, even from a monarchist perspective the independence of the United States is quite legitimate since it was recognized by King George III himself in 1783.
However, as a side note, US ownership of Hawaii is hardly legitimate. The Kingdom of Hawaii was an independent country which had treaties with all the major powers; the 1893 overthrow of the monarchy and 1898 annexation were in violation of international law. To his credit, President Grover Cleveland recognized this, opposing the unjust ouster of Queen Liliuokalini, and it was not until he was out of office that Hawaii was annexed.
The overthrow of the Bourbon and Hapsburg monarchies cannot be equated with the American War of Independence. The events of 1775-83 did not interfere with George III's position as King of Great Britain. But the French and Austrian republics displaced ancient monarchies, integral to those countries' heritages, laws, and traditions, whose last sovereigns never renounced their rights and could not have lawfully done so even if they had wanted to. Therefore they remain illegitimate, unlike the United States.