Good points and suggestions from Dale. Actually, these Moodle (or online) issues are similar to those you will find in a face to face school and classroom. Do people trust each other? How do you keep the honest people honest and put reasonable locks on doors to keep out most trouble makers?
If you have high security in your face to face classes then I would not do anything on the web. For example, High security means sweeping the room and surrounding areas for listening devices and having every student sign the "loose lips sink ships" oath and checking to make sure they live up to that pledge. In a really safe environment people know it is safe rather than trust it is safe
The real safety issue is what is an adequate level of protection and who on the outside really wants to know what goes on in your classroom between students. That is something for you to determine.
In the US we have a set of educational rules for teachers and administration called FERPA. Moodle can operate in a FERPA environment.
I work with one Moodle site that is on an internal network that has fixed IPs (that I think are actually assigned to MAC addresses of individual network cards on specific computers). There is no web access and people have signed a paper that they will not share outside of the group. That is fairly secure but not absolutely secure. But it is safe enough for the purposes it is being used for.
Good luck Chris