I agree with Eddie. Mick makes a point that is correct, but in this case Eddie means that none of Daniel Boone's descendants lived in Vermont and therefore none were born there. If you can find "The Boone Family" by Hazel Atterbury Spraker, there is no Stephen named as a descendant of George Boone. She identifies a Stephen Boone in NC as one Boone found in 1790 NC census and is NOT related to the family. I would therefore state that your Stephen is not related to Daniel Boone. My copy of the book is a 1922 edition, there are other editions in 1974 & 1982. You can purchase an ebook of one of these for $30 on Goggle Books. You should also search for the Boone Society web page and email them. I found them to be very responsive in my case. My mother is a Boone, and cousins had her family as descendants. She is not.
Good luck, Mike