The 1880, 1900 and 1910 census records for Amedee Frilot and his family identify them all as mixed race. The 1870 and 1880 census records for his father Prospère Frilot and family also identify them as mixed race.
Prospère's father François and paternal grandmother, Rosette Boutte, are identified as mixed race in 1850. There are no obvious census records for Prospère's paternal grandfather, Claude, but it appears that both his parents were born in France, so I would guess that neither was mixed race. Prospère's mother and maternal grandmother are identified as white in 1850. You can dig back through the records for Amedee's mother Adeline in a similar way, but in 1850 both her parents are mixed race.
It is not until 1920, when Amedee moved his family to Los Angeles, that we start seeing them identify as white. Although he died in 1922, his family are identified as white on the 1930 and 1940 censuses, as well.
I've seen this same pattern in my own family history, where a family changes how they identify when they move. How mixed race people were identified in historic records has a lot to do with how others perceived them, maybe who they marry and how that effects both cultural identity and labeling, and so on. Of course, racism is also a huge factor and many mixed race families would "pass" for white if they could to avoid segregation, discrimination, etc.
The bottom line of all that is that it isn't wrong to say that Amedee is part of U.S. Black heritage—and it's not completely correct to say he was just white or caucasian either. And the family was also Creole, Cajun, Free People of Color and possibly other things!