Dear Dennis,
The best way to prove or disprove this is to gather information on your grandfather & great-grandfather. Do you know approximately what year and where Luther Bryan was born? USA? Do you know what his father John A. Bryan's wife was named? If the family unit can be located in a US census record, it should be easier to assure we have found the correct people.
Here is an example of a census listing for a family where the son is Luther and the father is John Bryan:
"United States Census, 1910," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:M2S2-DZ1 : 29 October 2015), Luther Bryan in household of John Bryan, Justice Precinct 3, Nacogdoches, Texas, United States; citing enumeration district (ED) ED 98, sheet 14A, NARA microfilm publication T624 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,375,594.
Let us know all the deets (details)! We may be able to help. -NGP