The date on the FindAGrave memorial is probably his burial date, not his death date.
DIED - Yesterday morning at the poor farm, William Smith, colored. Deceased was 35 years of age and had been suffering from epilepsy.
Idaho Daily Statesman
Boise, Idaho
28 Aug 1903
p. 5
I also found...
SENT TO THE POOR FARM. - Sheriff Agnew send William Smith, a helpless colored man, tot he poor farm yesterday. Smith is said to be mentally unbalanced.
Idaho Daily Statesman
Boise, Idaho
14 Mar 1903
p. 5