They did, but ESPN's reach and control of college sports is leaps and bounds beyond anything it was 30 years ago. Before, they were reporting sports (often with a humorous savvy), and working as a scrappy media startup to grow their network. Now, they more or less own college sports as an entertainment brand, so they're much more invested in hyping it, pushing it, and getting people to pay for access to it.
Even if Tennessee got attention (which it did), the pervasive marketing of new media, social media, and influencers didn't exist back then. It was ESPN, ESPN2, and eventually ESPNU. That was it. Now, ESPN is like marketing on steroids. They've closed their grip on college football, which makes them the king. I wish I could share what it was like to not have ESPN calling the shots, I really do. I know it's all about the money, but back then at least it was much more about the games and much less about ESPN itself. I miss those days.