I just came across this comment on Twitter: "During the Middle Ages, university students carded and spun wool and flax during lectures, and it was often mandated."
I do realize that there are a lot of myths about the medieval period, and that "medieval period" is a vast swath of time during which nothing was static. But that claim flies against what I understand about draconian attitudes toward studious discipline. I also would have thought that university education in this age was a position of extreme privilege - would that really have been a population which engaged in textile production? Also, I would have thought that this kind of labor was heavily gendered - not something that men generally would have been engaging in at all.
I think your instincts are right, and that this is, not to put too fine a point upon it, kind of silly. Medieval women (throughout the 1000-year period) spun thread--early middle ages on the drop spindle, later middle ages on the spinning wheel. In both cases preparing the wool or flax for spinning would often be in the household. Weaving, which was primarily a female occupation in the early period, becomes a male activity upon the invention of the heavy pedal loom that gets used for commercial cloth-making starting in around 1300. Spinning, though--that was women's work. There are many examples of medieval paintings, particularly in the marginalia of manuscripts, that depict women carrying their drop spindles and distaffs around with them while they do other household chores. Little girls started learning to spin as soon as they had enough coordination to hold the spindle.
Another reason for objecting to this statement is the well-known exclusion of women from university educations. Young men who entered medieval universities were, as you say, generally of a higher class, and often were in minor clerical orders. Some of them started university as young as twelve. Spinning would not be an expectation for this group.
I have never seen wool or flax preparations in any records I have read from medieval universities. That doesn't 100 percent guarantee it didn't happen, but it's highly unlikely.