I don't think the two are very comparable, MBRO.
That "disastrous decade" of LSU's included two consecutive years where they were champions or co-champs of their division, a 10-2 season that ended with a Peach Bowl win over Clemson, a 9-3 season that finished with an Independence Bowl victory over Notre Dame, and another winning season (7-4) that included a bowl win over Michigan State (yes, ironically, a Nick Saban-led Michigan State).
So that "disaster" is a far cry better than the Vols' Dark Ages from 2008 to 2017.
And I know that's not the point. The point is, they didn't have coaches who met their expectations, so they went out and hired a known Killer (Nick Saban).
Except that Nick wasn't so much a Known Killer at that point. He was a very good coach who'd had relative success at a place that hadn't seen much lately. In other words, at that point in time, Nick was what Dan Mullen is today. A guy who had success at a "lesser place" and who had high expectations.
As for Nick's high salary at LSU being proof that the Tigers were willing to go out and "pay for excellence," his salary was in fact doubled: to $1.2M/year. See, a big part of that was a sudden inflationary bubble in head coach pay...those were the few years where things ballooned from sub-$M up to the multi-$M range, in a short period of time. Nick Saban benefitted in part by riding that bubble. LSU did expect much of him...but it's not like they knew he was destined to win multiple national titles. At that point, he hadn't even won a Power 5 conference championship. Heck, he hadn't even won a P5 division title.
So I personally don't think saying "LSU" helps make Hillbilly's case. It's probably the best play he's got. But it's not really an answer to Behr's question. Not a really good one, anyway.
I'd say, based on what we've seen in this thread so far, you'd have to conclude: no, that has never happened, Behr. The fan base has never forced an administration's hand by declining attendance, and made them go out to hire a Killer.