Whodunit

In a communications class I'm taking, there was an exercise to test quality of listening. The instructor read a paragraph, after which the class answered a series of true/false questions about what they had heard. Then the whole class discussed the answers they had written down.

The paragraph went something like this:
The professor finished drawing up the final exam, and got ready to leave for the night, putting the exam into a desk drawer. Suddenly, a tall, broad person appeared at the door of the office, demanding the exam. The professor opened the desk drawer, and the contents of the drawer were picked up. The figure fled down the hall. The professor reported the incident to the dean immediately.
One of the true/false questions was
"Was the man who opened the desk drawer the professor?"

Some students had answered true, some false. One of the reasons given for answering 'false' was that the question used the word "man", and there was no evidence that the professor was a man.

I answered 'true', since I remembered that the professor had opened the drawer. Looking back at it, I felt that the structure of the question strictly implied that a man had opened the desk drawer, so there was no longer any ambiguity about the gender of the professor. A female student said this was a sexist assumption. I replied that if the question had said 'Was the woman who opened the drawer the professor", then that would have implied the professor was a woman, so there was no sexism involved.
Still, others argued that it was fair to say the answer to the question was 'false', because it contained an otherwise unsupported presupposition.

Thinking about it now, I would say that there is a difference between the answer to a question being 'false', and the question itself being false. But would it still be fair to answer 'false' in either case?

What do you think?

john