SQL DB Permissions so anyone can modify the DB
Add the Windows Group, Everyone, to the database db_owner role, if you're really certain you want anyone and everyone to be able to do anything they like to the database. Take a backup of the database that you will then distribute to the class. After you take the backup, remove the group from the db_owner role.

The only gotcha is the students need to have their instances configured with Windows Authentication enabled. 

Windows Authentication stores the SID of the Windows principal in the database; in the case of the "Everyone" group, the SID is the same on all Windows machines.