Not every university / university class is big. Most likely explanation is that they simply said they live together.

Ah, that'd make sense. I would just think that they wouldn't mention it if they planned on cheating lol.

Back when I worked first line at a University, I had access to the student records system (so that I could verify students if they required a password reset).

I was able to see current and past residence data, which I suppose could have helped me verify the student's identity ("what post code[0] do you currently live at?"), but I tried not to look at that information when possible.

Lecturers also had access to this system (it dealt with some submission data), so I guess they may have had access to view residency data?

This is just an educated guess based on my experience, though.

[0]: For American readers, think ZIP code