I think it’s in quotes because it’s a quote. The person identified himself only as a “student.” However, that has yet to be confirmed. So they can’t say he was a student—they haven’t confirmed it. They can refer to him as a “student”, because that’s quoting the individual.
Legitimate quoting is not done for individual words. The use of scare quotes is generally done to insinuate that the description is questionable.
Suppose that a congressman and his wife had spent the weekend at a hotel. If the hotel staff (being quoted) said that the congressman and his wife stayed there, would you expect only the word wife to be put in quotes like that? I think it's entirely natural for most people to take a completely different meaning from the following two (almost identical) headlines:
Congressman Jones and his Wife Spend Weekend at the Fairmont.
versus
Congressman Jones and his "Wife" Spend Weekend at the Fairmont.