Well, Dodd legitimately got mad over the 140 rule for scholarships. In fact, Alabama's President broke with Coach Bryant who SUPPORTED DODD'S position on scholarships. (The 140 rule stated you could have 140 scholarship athletes for football and men's b-ball - note that things like Title IX, passed in 1972, would later affect this stuff).
The Holt-Graining incident was played up by the press (Bisher) because they got jealous of Bryant beating them. Dodd didn't want to leave the SEC, but he felt he had no choice and couldn't compete.
It was a colossal mistake as everyone involved even at Tech today now admits. If they'd just been patient, Tech would still be in the SEC today and who knows - maybe S Carolina wouldn't....