Several episodes ago (IIRC, the one where Renly was killed) Davos convinced Stannis to leave Melisandre behind when they attacked King's Landing, because he didn't want people believing that he only won the throne by sorcery.
Also (IMO) Stannis isn't that enthusiastic about Melisandre and her Red God. He had to use her before because there was no other choice due to his limited support. But, after picking most of Renly's supporters I think he'd prefer to do things himself.
Ah, I forgot about that scene. I still find it odd that Stannis would agree to it, considering no one else knew of her involvement other than Davos. I take it Davos is dead now?
If you recall the story of how the Hound got his scars (this was in the middle of season 1, IIRC Littlefinger was telling it to Sansa), his brother Gregor aka the Mountain shoved his face in a fire when he was a child. He's absolutely terrified of fire, and fighting in the middle of the river burning with wildfire (when was much, much worse in the books) was enough to break him.
Edit: Damn, too slow.
He seemed to have no issue charging out of the gate even after the wildfire attack. It wasn't until some burning guy charged him that he lost all composure. I guess I just wasn't convinced that fire was the issue since they showed him fighting in and around it for quite a while before losing it.