I disagree that there was much Nebraska could have done to essentially "get out" of hiring Frost.
Frost was the NC winning former QB, apparently still friends with Osborne, and had just completed an undefeated season at UCF. Husker fans had wanted Frost back in Lincoln since Bo Pelini talked to him about leaving Oregon to be the Husker OC. You're right that the internal pressure on Moos would have ended, but he'd have needed a security detail to get to back and forth to work every day. Never mind ever appearing at any games, Moos would have gotten the loudest boos of anybody in Husker athletics history. Moos wasn't the golden boy and home town hero, Frost was, and very few people knew about Frost's "issues." There's no way Moos and UNL leadership win that PR mess by being nice and taking the high road.
The only way Nebraska gets out of the PR disaster of not hiring Frost is to "play dirty" and leak negative, but factual, stuff about Frost. (Not to mention hire somebody who won, and hope Frost fell on his face at Florida or back at UCF.)
Even at that point I don't know if it would have worked, absent the Huskers winning and Frost failing elsewhere, that is. Look at what happened after Frost finally got fired. There was a flood of negative stories about his time as HC. Everybody in the local media and around the program knew about those things when they happened, yet nobody wanted to report them. IMO, that's at least in part because their readers/viewers wouldn't have believed them, because until the end many fans didn't want to believe anything bad about Scott Frost.
EDIT: If Frost wasn't the hire, who do they go get? IMO, whoever they hired would have started with at least "1 strike" against him from the fan base. I don't think you get a Chip Kelly or another top coach to take the job in the midst of the PR fallout. I think it would have been Bill Callahan all over again, just for different reasons.