by Tony Box.
Wow, thanks Sonia! That actually worked.
I did a little more experimenting and all you need is the following:
Under Site Administration -> Courses -> Backups -> General Backup Defaults, you must set the defaults to at least have "include enrolled users" and "include activities" checked. If either of these are unchecked at the site-level, taking a course backup will not include user data, even if you check those two things on the individual course backup's page.
This definitely seems like a bug to me. I'm going to create a tracker issue for it.