That is probably a privacy policy that the rental company wants to follow.
I mean, if you called on the phone and asked, "Is this place filled with rich professionals who are usually gone during the day?" They might be cautions about telling you that.
Just go check the place out yourself.
No, fair housing laws do not prohibit the property management from answering questions concerning whether there are a lot of students living in the apartment complex.
However, students usually do not have kids, so stating that an apartment complex has a large number of students can indirectly be interpreted as acknowledging the apartment complex discriminates against families with kids. Or, if you have kids, and the manager stated that the majority of the tenants are students, then that can indirectly be interpreted as an effort by the proeperty manager to discourage you from renting at that complex.
It's really stupid, but unfortunately there are fair housing activist groups that send undercover prospective renters to apartment complexes. These undercover operatives' sole mission is to get a property management representative to make some statement, even a completely innocuous statement, that violates the fair housing act. As a result, property managers will almost never answer questions concerning the characteristics of their tenants.
If you want to find out what type of tenants are at the complex, then knock on a couple of doors, and ask. Tenants are perfectly free to discuss anything. Its only landlords and their representatives that are constrained by the fair housing act.