Hi Illium, this has actually resolved itself, and we can tell why he couldn't pick it up after the fix.
The NPC you pick up the quest from, Ujishige Daidouji (the samurai), originally gives you the quest when he is in a different location to normal - i.e. near the forge instead of the entrance. He moves to the forge at a certain point in the story, where he gives you that quest, then moves back to his original spot later.
My friend couldn't pick up the quest from him in his original spot. We progressed the story further (destruction of the town), and Ujishige moves back to his spot near the forge where my friend was able to pick up the quest.
So it seems that that specific quest is also tied to his location - we were lucky, but if someone had already progressed past our point in the story, they might not be able to pick up the quest again.