The Volunteers have won 6 national titles, not two, in 1938, 1940, 1950, 1951, 1967, 1998. The last one was a year after Peyton Manning graduated.
They apparently decided to use AP national champions.
Tennessee has won six national championships from NCAA-designated major selectors.[5]:112–115 Tennessee claims all six national championships.[6][7] The Associated Press has acknowledged Tennessee as National Champions twice, but the #1 Vols lost in the Sugar Bowl in 1951 after being named AP and UPI National Champions due to the polls being conducted before the bowl season prior to 1968 and 1974 respectively. The 1938 and 1950 championships, while not AP titles, were recognized by a majority and a plurality of overall selectors/polls, respectively.[8][9] Tennessee has also been awarded national championships by various organizations in eight additional years of 1914 1927, 1928, 1931, 1939, 1956, 1985, and 1989, though the school claims none.[10]