In my family tradition, William Matchett is identified with William Perkins Matchett Sr., son of Capt. John Matchett and his wife Elizabeth Perkins, born 26 September 1774. A couple of these names was indeed married in Boston -- but not until 1786. In nearly three years of searching I have found nothing at all to independently verify the birth and parentage. It is true, however, that from about 1810 he began signing his name with the middle initial P; my aunt even has a few examples.
He married Joanna Stetson, the daughter of John Stetson and Joanna Green, in 1802. (Descendants of Cornet Robert Stetson of Scituate, no. 3 (1956): 13) They lived first in Boston and then in Brighton, where he probably died about 1848 and she was still living in 1850. (census, p. 83)