Don't think Nicklaus and Player should be on the list either.
Correction made. Thanks, yippedagain.
Doing my homework in arrears, I've now scoured the list of past British Open champions -- back to the days of Young Tom (Morris, not Watson) -- and found one more U.S.-British Open same-year Open Champion -- Gene Sarazen. So that would leave the five in my edited post (Jones, Sarazen, Hogan, Trevino, Watson and Woods).
Can anybody else find another same-year dual winner?
To save you a little trouble, five-time British Open winners Vardon and Thomson didn't make the grade, nor did four-time winners Hagen and Locke. Palmer won his British Opens in 1961 and 1962, but got his lone U.S. Open in 1960. And four-time U.S. Open winner Willie Anderson never won the British (it was quite a boat ride in the early 1900s -- expensive, too).