I still think he was looking for Riddle's trophy (the one Ron barfed on).
Like the diary, he made the trophy a horcrux when he was young and arrogant, then thought better of it years later. He can't trust anyone, not even his "most faithful" death eater, to steal it for him.
Griffindor's sword has already crossed Dumbledore's mind, and I'm sure he examined it and determined that it was not a horcrux.