Texas played Alabama this year and is set to play Alabama or Michigan if we beat Washington. We have games against Michigan, OSU, and Alabama in the coming years. I listed out our record against the top cluster of schools in the "weeks top 5 versus weeks in poll" graph. Some will want to add another blue blood or drop Nebraska, but I simply followed the numbers. I grouped those with over 700 weeks in the AP poll (and over 250 in top 5) as blue bloods and those with over 350 as helmet schools. Some will obviously balk at my including aggy as a helmet school, but they meet the criterion. The cutoff as set provides a historical top 25.
8 Blue blood (>700 weeks in AP)
Texas
Alabama 8-2-1 (.773)
Michigan 1-0-0 (1.000)
OU 63-51-5 (.550)
OSU 2-1-0 (.667)
Neb 10-4-0 (.714)
ND 3-9-0 (.250)
USC 2-5-0 (.286)
TOTAL 89-72-6 (.551)
non-OU 26-21-1 (.552) (I wanted to see how much OU biases our average, but they fall very close to the mean for other teams)
17 Helmet schools (>350 weeks in AP)
Arkansas 56-23-0 (.709)
Auburn 5-3-0 (.625)
Clemson 0-0-0 (n/a)
Florida 2-0-1 (.833)
FSU 0-0-0 (n/a)
Georgia 4-1-0 (.800)
Iowa 1-1-0 (.500)
LSU 9-8-1 (.528)
Miami 2-2-0 (.500)
Michigan St 0-0-0 (n/a)
Oregon 4-2-0 (.667)
PSU 2-3-0 (.400)
Tennessee 2-1-0 (.667)
Tx A&M 76-37-5 (.665)
Washington 3-2-0 (.600)
Wisconsin 1-0-0 (1.000)
UCLA 3-4-0 (.429)
TOTAL 170-87-7 (.657)
GRAND TOTAL 259-159-13 (.616)
Perhaps someone with more internet and spreadsheet ability and will may assemble a more complete comparison. Bottom line, though: Texas has a long history of winning football games against the best and against the best of the best.