Yes and no on this. It's true the game will only list one rival for TB teams, but you CAN have more than one rival. Even the regular teams in the game have some rivals that don't show up in their rival list.
In my dynasty, my TB team, The Dragons, replaced Rice in C-USA West. Which left me with Houston as my Rival. I then imported a second TB team (the Wildcats) who replaced Houston. Now we had EACH other (Dragons/Wildcats) as our rivals. Then I popped Houston back into C-USA West for UTEP and now I had both the Wildcats AND Houston as rivals, which is what I wanted.
The reason is The Wildcats took Houston's spot initially and had me as their only rival. When Houston came back in I picked them back up as my proper rival, but since the Wildcats had to also have a rival, it forced me to keep them as well.
But you are correct in that the game doesn't track rivalry wins/losses last time I checked, which sucks royally and makes bothering with rivals almost irrelevant.