You can do the quest solo, but if you tell them to support a faction that's the faction you are stuck with.
I see that now. He had not posted that by the time I made my original reply. So it stands on that ground, but maybe not for him.
Like I said when I first posted here, once you tell them who to support, you're stuck to that. Which is exactly what he did, which you would have known if you'd have read what he said.