It's a LIE!
First of all, There was no Vermont during the Revolution -- the area we now know as Vermont today was territory disputed between New York and New Hampshire in in 1777.
Governor Benning Wentworth of New Hampshire granted a charter for the township of Bennington in 1749 -- much to the chagrin of the governor of New York. Governor Wentworth continued issuing grants, and by 1763, 138 township grants had been issued for the territory that had become known as the "New Hampshire grants". These grants were hotly contested by the governor of New York and contributed to the mutual contempt of the New York and New Hampshire troops during the Revolution.
Vermont declared itself an independent colony in late 1777, but the territory wasn't officially relinquished by New York until 1790 and the new colony wasn't officially recognized by Congress until it became the 14th state until 1792.*
So, the infamous battle didn't take place in Vermont because there was no Vermont. But, furthermore, the battle did not take place at Bennington!
The "battle of Bennington" actually took place at a little town about ten miles Northwest of Bennington called Walloomsac (also Walmscott, Wallom's Kirk, Walloomscoick, Walmscock, Walloomsac, etc. -- I like to call it Wally's Socks). "Bennington" became the name associated with the battle because it was (and is) the largest town in the immediate area. Also, capturing the rebel military stores located at Bennington was the ultimate objective of General Burgoyne's force, so it stands to reason that the notorious battle took on that name.
The battle near Bennington was probably the most important battle of the Revolution. It was the first in the chain of events that led to the decisive battle at Bemis Heights (Saratoga) -- which in turn convinced the French and Spanish that the American cause had merit, and convinced them to declare war on England. The American Revolution quickly escalated into a global war that soon drained England's military and monetary resources and ultimately resulted in the Rebel victory at Yorktown in 1781.
Rand McNally, Atlas of the American Revolution, Rand McNally, 1975
Lord, Philip, Jr., War over Wallomscoick, New York State Bulletin No. 473, Albany New York, 1989.