It can. The problem is with their English translation. 要求 means what the teacher is asking for, or what the teacher is demanding. So the English would be better off as "Their teacher demands a lot", or "Their teacher asks for a lot". Your sentence is fine as well.
Leaving the "very" out was incorrectly marked incorrect. Often 很 modifying a stative verb/adjective (such as 高) isn't translated as very, even though it's a required element in the absence of another modifier.