I've had belts in old floppy drives do this as well.

I'm thinking you're right, it's a failure of the chemistry used at that time. The rubber wasn't stable, just long-term metastable. A common problem. No amount of testing would predict 30 year stability, so they had no way of knowing the composition would fail. Just like the bromine in the fire retardants that yellows cases. There is no way they could have predicted at that point it would happen given enough time. No one ever bothers to model the long term stability of something with a much shorter expected useful lifespan. It does create a really frustrating set of problems for preservationists and vintage collectors.

Unfortunately, I think it's a problem we're going to be contending with more and more as we move into yet more advanced materials. Apparently complex materials of the modern age don't hold up quite as well to the test of time as tried and true materials of previous centuries. Until we can figure how to deal with it there is going to be some pretty significant gaps in artifacts and collectables for this time period as a result in the future.