One of my brothers claims that the Indianapolis Colts were the same franchise that started in the AAFC, even though that incarnation of the Baltimore Colts folded after the 1950 season, and I say that the [modern-day] Colts started in 1953 as a new organization that got the assets of the failed Dallas Texans of 1952, which in turn, according to some schools of thought, were descended from various franchises including the Dayton Triangles-Brooklyn [NFL] Dodgers-Tigers organization, even though the NFL, according to Wikipedia, doesn't recognize any link between the Colts and the Dayton-Brooklyn entry and the Colts do not include records of any games involving the Triangles-Dodgers-Tigers club or the Boston Yanks-NY Bulldogs/Yanks-Dallas team[s].

You are right. The franchise from the AAFC folded after the 1950 season. The current Colts team came from the assets of the Dallas Texans franchise. My Dad was a Baltimore Colt fan. He now roots for the Ravens. He doesn't claim anything Indianapolis. Johnny Unites and most of the Baltimore Colts didn't either although the NFL does. Unitas and the HOF Baltimore Colts are actually in the Ravens Ring of Honor.