Thank you, Tim and Marcus, for your replies!
Before Moodle, I actually have used an online interface with students for years, so I'm aware of the inherent impossibility of totally preventing unauthorized file sharing. I wasn't really looking for a "foolproof" way to avoid copying, because you're right... it can't exist!
To strike a balance, though, I think it's reasonable to do what I can to secure my work. This is basically the eternal cold war of the internet: Criminals are going to do their best to steal, and good creators are going to do their best to protect their creations. We'll always have to try a bit harder to one up the other... I'm okay with that (don't have a choice ).
The mention of "permissions" is what I was after. Thanks for leading me in the right direction. I knew I had seen it somewhere... wasn't sure where... But I found it again. That answered my question.
Thanks again to you both!