Ever too late to bribe the Floating Nose?

[TedZeppelin]

Once a player has decided to fight the floating nose, can he change his mind and bribe it after he has lost the fight? My friend encountered the Nose and was unable to beat it, so he asked another player for help. Once they were both in the combat, I played Potion of Cowardice, forcing them to flee, which they couldn't do because the Nose doesn't allow it. At this point, they both said they would simply bribe the nose instead of suffering its bad stuff. I don't think that is allowed, and now we have a rules dispute on our hands.
I own the game, and so have made the ruling, but that will only hold up so long. Who is right? The Munchkin Trophy is at stake.