Are arguments of the form "what if everyone did that?" valid or not?

People often oppose some possible exception to the rules on the grounds that if everyone acted that way, the results would be terrible. For example, suppose that an honest and diligent student is in the hospital, and he wants to keep up with his school work as much as possible. His parents propose that he take his math exam from the hospital, and they'll monitor him during the exam. The school refuses on the grounds that if all students were allowed to do that, then cheating would be rampant because not all parents would be honest or diligent monitors. Is that a valid reason for refusing the exception to the rules? Does it signal concern for fairness and principle? Or does it amount to ignoring individual circumstances?