I agree that using the pop-up might lead students into confusing situations from a usability point of view, if they switch between the pop-up and the main window. However, that is a very different statement from staying that the underlying quiz/question engine has a bug.
No one if forcing you to sue the pop-up (it's probably my least-favourite feature, but I am not allowed to remove it.)
Anyway, I still struggle to see the problem: If a student is just concentrating on doing well in the quiz: the start it, type the password, concentrate on answering the questions, then submit, then there is no problem. It is only a student who messes around with things like switching windows, rather than just answering the questions, who can get confused. If students lose out by messing around, well that is not the worst thing ever.