I agree with you regarding the two noted; the other three all have the "TM" mark either to the bottom right of the S in TEXAS or to the right of Bevo's jaw.
A buddy of mine who once worked for UT-Admin told me that UT's fierce protection of all-things UT dates back to a lawsuit/negotiated settlement with DayGlo UT and the familiar block U and T that both schools use.
Apparently DayGlo sued Texas for exclusive rights to that logo and the negotiated settlement was for DayGlo to have exclusive right east of the Mississippi and Texas to have the rights west of the river.
Following that was a strong UT legal department push to trademark EVERYTHING that the University put out regarding logos, the color "burnt orange", phrases, etc.
UT WILL hunt down and pursue you like a dog (figurative speech here,
) if you step over the line.
What I've heard.
If you're going to produce and sell anything for a profit using UT-like logos or "Texas Longhorns", etc., or if you're going to name your new business "Texas Trash/Disposal" with a longhorn logo in burnt orange, get ready for "knock on the door" with a friendly cease and desist letter from downtown UT offices.