Pages cannot open file File
As it happens, the problem was very similar to another problem with preview I had previously, only that the error message was not claiming a permission issue.

The solution was, consequently, equally similar to that of the problem with preview:


I removed the sub-directory ~/Library/Containers/com.apple.iWorks.Pages/Data/Library/Saved Application State/com.apple.iWork.Pages.savedState
I quit Pages and re-started it.