It was late last night when I posted that answer. The pension application for Nathan Fay is in the file. He claimed service for 2 months in 1777, 1 1/2 months in 1779, 2 1/2 months in 1780, and six months in 1782. His depostion was dated 6 June 1833 in Vt. Then there are other papers including one that is a verification of the service of Nathan Fay from the Vermont Sec of State dated 24 June 1844. There is also a deposition from his sister Susannah Follet saying that her brother (born in 1760) had fought in the Revolutionary War. It seems to me that he was 17 when he first served and was 22 when he last served in the war. Acceptable service for the DAR goes from 19 April 1775 through 26 Nov 1783.
There is a pension verification in the file and his pension began on 20 Aug 1833. I think the confusion is that the pension in the file in fold3.com is noting a rejection, but that rejection is for sending more money to the family. There is a letter in the file from the lawyer of Mary Fay.
If you are interested I could scan a couple of pages for you. Pamela