Quiz

Your initial hunch is what I immediately thought of too. It must be a problem with the roles definitions, or overrides, or assignments.

The simplest way to capture all the necessary information is this:

1. Get the name of one of the students who has this problem.
2. Go to Admin -> Server -> Debugging, set Debug to DEVELOPER and turn on Display debug messages.
3. Go to the problem student's profile, and click the button to log in as them.
4. Go to the quiz that has the problem.
5. Go back to the problem user's profile. At the bottom there will be a whole lot of ugly debug output.
6. Starting from the line " [access] => Array" copy and paste that debug output here. Please use the 'Preformatted' style in the HTML editor, so the indenting is preserved. (That should not contain any personal information.)
7. Go back to Admin -> Server -> Debugging and turn off the two settings you turned on earlier.

Given that data, we should be able to work out what is happening.

(It is somewhat annoying that what I am working right now are some improvements to the roles interfaces for Moodle 2.0 (Development:Roles_administration_improvements_for_Moodle_2.0). When they are finished, diagnosing permissions problems like this will just take a few mouse clicks. Still, at least this post shows I am not completely wasting my time.)