My guess is that your character entered the village earlier, the quest was generated, but you didn't encounter the character at the time and then returned after selling the arrows, at which time you encountered the character.
As far as I know, saying he can't have the requested item "fails" the quest, but I don't know what happens if you don't have the requested item anymore. Thus, I'm not sure you can fulfill the quest by finding the requested arrows and return with them later, but if the quest log shows the quest is open I assume you can. Thus, check the F2 log to see if the quest is open before going through the process of searching (and given how rare superior arrows are, you'll probably run out of time before finding any anyway).