I’m not sure the teacher is, technically, correct here.
Unless the surveys were given on oath, under penalty of perjury and/or with explicit disclaimers that any information provided could/would be used against them, the students wouldn’t have the right to invoke the 5th.
However, had any of the students provided incriminating disclosures in the survey and those disclosures WERE used against them, they (and their parents) would have one heck of a good legal case (based in part on the 5th) against the school.
The right to remain silent applies every where except if you are under oath. In that case you may only take the fifth if the answer would indeed incriminate you.