The topic under question is the respiratory hygiene of dormitories as compared to living in a house or other living condition. The N that is under consideration is the number of dorms, and the people who live in those dorms.

There are pros to having the study done on a single university if there is a large enough sample of students and dorms. Since they all were in the same university, it makes it easy to isolate for the dorm variables in a way that wouldn't be as easily accomplished with multiple universities.

[Same university, different dorms] isolates for dorms, keeping the university constant.

[different universities, different dorms] does not inherently isolate for just dorms, since there may be compounding factors present due to known or unknown variables present in different magnitudes in different universities.

Some universities have many dormitories. My alma mater had 18 different dorms and an 30,000-40,000 undergraduate student enrollment. It was like a mini city, complete with its own area code, police department, and post office. If you lived in a dorm, you could go a whole semester without stepping foot off campus if you wanted to. The vast majority of undergraduates lived in dorms during their underclassman years. You can get good data from 18 different dorms and tens of thousands of students. And arguably you can get good data with an even smaller number of dorms and students.