I meant this as a real question because I know very little about Hawaiian music. I just happen to own this early Hawaiian recording on Victor. I was hoping you could tell me more about when exactly the Royal Hawaiian Troubadours made these recordings. You are definitely not the only one online who claims that they were the first Hawaiian group that were commercially recorded.
I've now checked Tim Gracyk and Frank Hoffmann's "Popular American Recording Pioneers" (2012). On page 119, they write, "By 1904 some Hawaiian troupes were performing in mainland cities, including New York, where American's Hawaiian recordings apparently were made in late 1904 or early 1905. Over two dozen performances were issued on a series of 10 5/8 inch blue single-sided "Indian Label" discs. [...] The American Record Company catalog dated September 1905 introduces the Royal Hawaiian Troubadours as an "orchestra and double quartet of native Hawaiians whose music has charmed America. ... The Troubadours are in America on an educational tour. ... By special arrangement we have secured the following list of the first and only records made by Hawaiians in America."
If Gracyk's dating of the recording sessions is right, the American Record Company's promotional hype was not true.
What about W.S. Ellis (a.k.a. William Kuali'i Sumner Ellis) and Ellis Bros. Glee Club? They recorded for Zonophone in July 1904 (DAHR). These recording were released in 1904 as Victor 15008 - 15049; (a 1910 repress of Victor 15014 is here).