I have never understood why there needs to be anything but the shape of the state with TECH inside it. The shape IS the LA, La., Louisiana, etc... It doesn't need the extra wording in front. We have a very recognizable state shape. We aren't Wyoming or Colorado. People know the boot....
You are correct. That doesn't exclude those companies from also using other logos, or that logo with words.
The The State-T is great, its the University's main logo. LATECH logo is also fine, its a sub-logo, and refers to the athletics, its fitting enough since that is typically what is on the score bugs on TV or the scoreboards. Keeps people from trying to put LTU anywhere. And then there is the Dog and Techster logos that refer to the specific men's and women's teams that need differentiation.
Its all ok to use.
Time is your friend. Impulse is your enemy. -John Bogle