I would say yes, they would be wrong. "Water on the knee", for example, is a layman's term for a medical condition. We can say "What is 'water on the knee'?" but not "What is a/the water on the knee?" or "What are waters on the knees?"
I don't think the quotation marks are required but I do think it gives an extra clue to someone unfamiliar with the term to recognize it as a term.