"at the whim of a hat".

My first assumption was that Bush had "drop of a hat" and "rim of a hat" floating around in his mind, and somehow they got blurred and combined.

Butb then I thought, perhaps he might have had some recollection of Stagolee lurking in his memory?:

What do I care about your two little babes,
Your darling loving wife?,
You done stole my Stetson hat
I'm bound to take your life;
He was a bad man,
That mean old Stagolee.

I wonder if it'll make it into some future editon of the Oxford English Dctionary as a new meaning for "whim"?