montgomery county is the home of virginia tech university.
Ohh, OK. That does explain it.
But what about Floyd? Latte liberals or spillover?
I note that Floyd, with Carroll and Grayson on the same mountain, was a hotbed of violent unconditional unionism during the civil war - we're talking "not safe to wear gray in after dark" - , and has been Republican almost ever since.
And checking the election history since 1960, Floyd seems to be where that tradition is strongest.
It was Nixon's second best county in the state that year, btw, just barely pipped by Rockingham.