Has a FIBA World Cup game ever ended 65-64?
Exactly once. On September 7, 2014, Turkey beat Australia 65-64, and no FIBA World Cup game before or since has ended that way. When it happened it was a scorigami, the first 65-64 in league history.
That makes 65-64 the 240th most common final score out of 863 that have ever occurred in FIBA World Cup. One point away, 66-64 has happened 4 times and 65-65 has happened never.