I am not Bama or Aggie ... we have 4 - 1942, 1980, 2021, 2022
I get the joke and agree (especially that one title Alabama claims where they lost 2 games and are not even recognized as the SEC Champion).
Tennessee is an interesting setup from that era and fun to talk about. They had 6 (if you take out bowl games it is 9) undefeated seasons with Neyland at the helm but only 1 AP title. Interestingly, the year we won the AP title, we don't deserve it and we lost the bowl game. In his era, you often had to go unbeaten or have a great season, win the bowl game, and then go unbeaten again to win a National Title unless you were Michigan, Notre Dame, or a team in a good media market. Most of the SEC Champions had to do that.
In 1950, Tennessee went 10-1 and won the bowl game over the #3 but got nothing. So when Tennessee went undefeated in the regular season 1951, the AP gave Tennessee the National Title but they lost the bowl game. Also from a performance aspect, the 1950 team was an overall better team. 1950 Tennessee really deserved that AP title and not the 1951 (or 1938 which I will explain below).
With UPI poll, the same thing happened. Tennessee went unbeaten in 1938 but got nothing and then went unbeaten and unscored on in 1939 and got UPI National Title (equivalent to today's coaches poll). However, they went on to lose 14-0 in the Rose Bowl to the USC Trojans. Interestingly though, the best 2-3 players didn't even play in the Bowl Game because Bowl games were treated basically like they are treated now and not taken seriously.
1920s, Neyland had multiple undefeateds with no championships. So often teams would get AP titles in NOT their best years but based on performance from previous seasons that were built up.
Of course about 10 years ago, Tennessee started claiming 6 National Titles and included 1938, 1940, 1950, and 1951. They also claim 1967, I think, but I don't see that one. 1940 is an odd one to claim because they finished #6 (although they were 10-1) and the sole loss was to Boston College in the Bowl Game. I think they have an argument at 1939 based on the facts above that they really didn't travel with the full team to the Rose Bowl. Plus it is the last team in CFB to go undefeated and unscored on in the regular season.
I just looked up Georgia and they claim 4 (1942, 1980, 2022, and 2023) but you have 4 unclaimed ones in 1920, 1927, 1946, and 1968. The 1946 one looks legit and I think you could have argument for that one.