Well, they did finish 1st in about every single poll at the conclusion of the regular season. Isn't that how many national championships were claimed by many teams in the past? Going by polls before the bowls even played out?
I know some of the so called 6 national championships UT claims they won were because some obscure poll had them ranked #1 at the end of the regular season (not the AP or even UPI poll mind you). Ignore the fact they went on to lose the bowl. 1967 comes to mind.
And no, I don't really buy into that those 6 claimed national championships claimed by UT were all legitimate.