As is well known, to rickroll is to post a misleading link to this video. We can define rickrolling in answer to a question precisely: To rickroll is to provide a link to that video instead of answering the question.
Suppose someone asks "What's a rickroll?" and I respond with a link to that video. Have I just rickrolled them?
By virtue of the meaning of the question, I've answered it (demonstratively) if and only if I've provided an example of a rickroll.
But by the definition of rickrolling, a link to that video is a rickroll if and only if it does not answer the question.
Paradox! There may be some actual point here about terms that are defined by their relevance to the conversation or context.
...in any case it may not have been the smartest thing for an untenured professor to send the link to his entire department.