The area that is now the state of Vermont (based on "vere mont" -- the French translation for "green mountain") was a disputed territory long before the revolution. The region between Lake Champlain in the west and the Connecticut River in the east had been subject to competing claims by three different British jurisdictions (the Massachusetts Bay Colony, the Provice of New York, and the Province of New Hampshire) at various times as far back as the 1660s. Because of the rugged terrain and harsh climate, it was basically ungovernable by any of the three -- and the "Green Mountain Boys" under Ethan Allen was an informal militia that effectively functioned as the only legitimate form of government since its inception in 1770 (some years before the revolution began). The basic purpose of the militia at the time was to allow settlers in this region enforce their New Hampshire land titles against the wishes of the British government (which had awarded these lands to the Province of New York).
Allen and his fellow leaders of the Green Mountain Boys saw the success of the colonists in the American Revolution as a means to negotiate deals with both the British government and the new American government to secure the best arrangement with either one -- to have Vermont join either Lower Canada as a British colony or the new American government as a U.S. state. At the time, the status of Vermont was so uncertain that it was conspicuously absent from the original Thirteen States.
Vermont's historical influences can be seen even to this day -- as Vermont still has a reputation for being among the most libertarian of all states in the U.S.
I know this is a long-winded reply, but it's basically a long way of saying this: Ethan Allen may have carried out the raid on For Ticonderoga "in the name of the Great Jehovah and the Continental Congress," but the Continental Congress had absolutely no authority over the Green Mountain Boys and would have been completely powerless to do anything if he had refused to carry out the raid (hence the captain's question to Allen about "by whose authority that he demanded it [the surrender of the fort].
(On a side note, one of my ancestors, Major Amos Morrill of the New Hampshire Grants, was with Allen and Arnold when they took Fort Ti by stealth in 1775. Of course, there's no mention in the family genealogy that specifies exactly where he was when Johnny Burgoyne's expeditionary forces showed up to retake possession, virtually unopposed, in 1777. (g) )