Enable home directory sites in Lion server?
Found it: The UserDir module in Apache2 defaults to public_html. So ~studentname was being directed to /Users/studentname/public_html. Which doesn't exist in any of the users' folders.

What does exist is /Users/studentname/Sites, so I just added this line to the httpd.conf:

UserDir Sites


...and it's working perfectly now. Awesome!

Many thanks to @bmike for pointing me in the right direction.