Oh, It's An Irish-Catholic Thing
This 'one'. That 'one'. Another 'one'. Chris Matthews says that it is an old Irish-Catholic thing. And I am inclined to agree. John McCain was born an Episcopalian Scots-Irish American. But he would be old enough to have picked-up on this use of the word "one."
School teacher: "You're a smart one."
Grandma (let's call her Rose): "Which one of you little devils broke my coffee mug? That one!"
John McCain:
And Mocean Worker quickly produced this great little diddy (H/T to Driftglass for finding this):