In that quote, it refers to the shrine. However, unless the other ghost is a dualistic second aspect of Yuuko, both the shrine and the ghost should be older than the school. After all, that part of the shrine seemed to be sealing something. I say a part of the shrine because we didn't see anything so big that it would have claimed the whole hilltop, so I assumed there could have been more. Though now that you said it, it's of course possible that's all there ever was and the school was built around it. In that case it was quite an ominous place, if the whole hill was claimed by a small shrine sealing away some demon...