I think it marginalizes the idea to say that firing him if he lost the first round game would be "basing it on one game". It would be basing it on three first round games, and three seasons worth of games where we didn't even get a chance to win a first round game. Tubby had us at one and done in year two, and it is not unreasonable to expect some kind of better playoff performance over the course of the next four. At some point there is a straw that breaks the camel's back, but a firing would be based on the body of work, not that last game.
Also, the way NCAA runs its playoffs, being a national champion and not being one comes down to one game. In the tournament, those are big one games.