The son of James Madison Bassett (1830-1903) and Carrie Hazeltine (1858-1943), R.H. Bassett was born Bernard Hazeltine Bassett, but he legally changed his name to Rex Hazeltine Bassett, often going by either R.H. or Reginald.
R.H. Bassett was the uncle of landscape artist Oliver C. Bassett (1927-1975). And he was the brother-in-law of book author Dorothea Castelhun Bassett (1889-1950). Dorothea was the 2nd cousin of Charles Darnton through his wife Maida Castelhun, and she was the 2nd cousin thrice removed of Scott Trimble.