Is "there are students" an option? Because I've noticed with sentences using "там", "these is/are~" is more natural sounding.
This sounds like a response to "де студенти?/where are the students?" which is asking about the location and not whether there are or not any students.
Yeah, I was starting to see the fault in my logic as I got further into the section. :P It's more about location than actual presence.