Thanks, Nigel.

I could have saved us all a lot of trouble, if I'd checked the "Traditional Tune Archive" first:

'John Hartford ("The Devil's Box") found that the "Grey Eagle" title for the melody known as "Miller of Drone (1) (The)" became attached to the tune in America following this famous late 1830's race between horses known as "Grey Eagle" and "Wagner." The race has been documented and took place in the Oakland Racetrack in Louisville in 1838. Soon afterwards a tune folio celebrating both racehorses appeared (a copy of which is in the possession of the Center for Popular Music at Middle Tennessee State University, Murfreesboro) with both "Wagner" and "Grey Eagle" as well as the now-obscure "Oakland Racetrack." In fact, the ancestral melody "Miller of Drone (1) (The)" melody gave rise to a tune called "Gray Eagle Cotillions" by William C. Peters, published in 1840, named for the horse in the race in Louisville.'

On the other hand, the year of the race referred to was 1839, not "1838" as the TTA asserts.