Ok, so I kinda screwed this up.
I achieved background scrolling by keeping my character at a fixed point, and moving the background. It worked fine, until I added an patrolling enemy.
He syncs with the background when standing still, but I haven't figured out how to make him patrol without falling out of sync with the level. One possible solution is to add collidable objects, but then he'd behave more like a lemming.
Is there a better solution?