What exactly "unauthorized access" means is still being ironed out in case-law. Just because you have access to something doesn't mean that you are authorized. Prosecutors have attempted to push "hacking" charges against people for accessing something on a shared drive (with no technical permission restrictions) because the employee was not "authorized" to view said file.
Just because the students had the admin password doesn't mean that they had permission/authorization to access that teacher's physical computer. Even if they had permission to do that, they probably didn't have permission to access the wallpaper settings.
This is really a failure of the laws in question to be less broad, and a failure of prosectors / cops to show some sort of restraint.
- MANY students had the admin password. It was freely passed around for the students to complete work from home remotely.
- The admin password was the last name of a popular teacher.
- He logged in using the same admin password all the other students use and freely have access to.