Yes, people who get attack have the option to fight. If they don't want to fight, they can wait for reinforcements. And if they don't wait for reinforcements, they can bribe you to back down. That is, i think you have to option to accept or decline the offer, else it would be the all powerful anti attack tool(except for logging off) if the game forces you to take the bribe.
"The flower of friendship blooms even in hell. On the sand where waves come and go, it leaves its petal as a memento. We will make it bloom again someday, The Okama Way!" - Mister 2, Bon Clay