There's little doubt that Barber shot down Yamamato's Betty. Lanphier could be a shameless self-promoter. Lanphier's claim of shooting down a zero on that mission was officially disallowed after post war records proved that none of the Zero escorts were lost. Additionally, he tried for years to get sole official credit for Yamamoto, but the Air Force refused. As a result, Lanphier never made ace status coming up short with 4.5 kills.
Lanphier's after action report contained contradictions and was disputed by many of the pilots who flew the mission and Japanese survivors who were interviewed after the war.
Author John Stanaway researched this story and his evidence establishes that Lanphier probably never even got near Yamamoto's Betty, much less fired at it. He probably fired on the other Betty bearing Yamamoto's staff.
My regards,
Widewing