East Tennessee was always the majority, Dixiecrat region of the state, going back to the Civil War. It wasn't going to vote for Nixon. Not surprising Wallace did really well there, as Humphrey was a Northern Democrat, and in the South that wasn't going to get him many votes against the Southern Democrat Wallace (officially ran as the American Party candidate, but everyone knew what he really was- a Democrat).
Basically, back then, especially in the South, people had really strong identifications, and it would take a really huge calamity to really pull them away. Hell, there were still a few McGovern counties in Tennessee, even though he was a "crazy" Northern Democrat who supported acid and abortions.
East TN was one of the strongest GOP regions in the south. Look at the map again. Nixon swept E TN