Texas won it 63 and 69, Arkansas was #1 in UPI in 64 and should have been in AP, which didn’t vote after the bowls; Arkansas won and Alabama lost to Texas. Texas was regular season #1 in '70.
I wouldn’t say the SWC was clearly the best conference, but it was as good as the SEC or anyone else. Really the Big 10 had more of a reputation as the best back then. But the SWC was as good as anyone. I remember in '79 one writer thought it was such a good conference that he gave UH, Texas, and Arkansas each a 1/3 vote for #1.