Did some digging, we lost to Nebraska in 1971 Orange Bowl, they were awarded the NC because both the #1 & #2 teams lost their bowl games,Neb. was #3.
This is interesting from Wiki:
In April 1970, Congress passed the Public Health Cigarette Smoking Act banning the advertising of cigarettes on television and radio; in order to allow the New Year's Day football games to keep their already-sold cigarette ads, the prohibition was set to begin on January 2, 1971. Airing in prime time on the East Coast, the 1971 Orange Bowl thus became the last televised sporting event to carry cigarette ads, the final one (for Winston) airing at 10:54 p.m. (The very last tobacco adverisement, for Virginia Slims, was shown at 11:59 p.m. during a break on The Tonight Show).
This post was edited on 9/13 at 4:10 am