The question really has several parts.

First, the performance itself is likely a public performance, which implicates one of the exclusive rights held by the copyright holder.  But it sounds like the performance took place in a teaching situation, so it is likely permitted by the exception to the public performance right for face-to-face teaching.

Another question is what was performed.  If it was music, and the campus has blanket performance licenses from the major collective rights organizations like ASCAP and BMI, the performance, of course, but likely also the recording, may be permitted.  If something not covered by any campus license was performed, the recording and the (very limited) distribution would have to be justified by fair use.

Based on the limited facts we know, I think the fair use argument might be pretty solid.  Presumably the purpose was non-profit and educational, and the potential impact on the market for the original would be negligible. The second and third factors might count against fair use, but courts tend not to weigh them as heavily as the first and fourth in most situations.

As with all fair use situations, this is a matter of judgment; if I were the instructor, I would be comfortable doing this, subject to all the things we do not know about the material used and the circumstances.  Others might not be.  It is also helpful to remember, with fair use, that if you change the facts, you change the outcome.  For example, if the student posts the recording of her performance to a social media platform, the analysis would be different.  Especially true if she is performing the latest Taylor Swift song, to take just one example (why, by the way, am I being bombarded with ads for Taylor Swift’s new album?  I have never bought her music.  Never.)

If I may, here is a related shameless plug – ALA Publishing will soon release “Coaching Copyright,” edited by Erin Ellis and me.  The first chapter, which I wrote, walks readers through a five-question framework to analyze any copyright issue.

Kevin