There's plenty of info about the health issues of balls (Meanie's linked a great thread for that) but I've not seen much on the natural behavioural aspects of chinchillas & the use of exercise balls ............ so I'm going to tackle the issue from that aspect, if I may.
From a purely behavioural point of view, one of the biggest problems with the 'deathballs' is that chins, unlike hamsters or other small furries, don't actually run in a straight line. They are curious creatures who like to bounce, jump, dart around & they can't do that in a ball - I think it is one of the reasons they don't look 'comfortable' in them.
If you consider that a chin's back feet are strong enough to propel them up to door handle height, that they love bouncing off walls, that they often zig-zag around, I think that balls are totally inappropriate for a chinchilla. They are just not 'straight line' animals - they are designed as rock hoppers.
Hamsters & guinea pigs generally scurry about in a straight(ish) line. Chins are the opposite, bouncing about like furry fleas, intent on getting where they want to as fast as possible & usually by the most 'interesting' route. They like to hide in small holes, potter about in tubes, cardboard boxes, 'investigate' (read: chew to destruction) anything that takes their fancy (new shoes? YUM!) etc.
Given the opportunity, a chinchilla in a safe environment will generally explore every cm of the area; the walls (ping!), anything they can jump up to, the furnishings (electric cable? Oooh good - mine!), the nearest available human (you'll do as a springboard or can I just sit on your shoulder & reach out to that place you don't want me to go? .... ah, yes I can - ping!)........ watch a chin for long enough & it becomes obvious that balls create an environment which is totally opposite to a chinchilla's normal behaviour.
They need enough space around them to sit up, to hop, to jump, & to explore - all of which are not possible in a ball, no matter how big it is.
Add to that the fact that chinchillas are generally pretty agile (yes, they sometimes bump into things & occasionally miss their target when jumping but they are pretty well controlled when moving) & need to be in control of their immediate environment - a chin which cannot balance properly & jump as they wish is not exhibiting normal behaviour.
The other issue which needs to be borne in mind is that issue of prey vs predator - chinchillas are naturally cautions/nervous animals who will, at an unusual sound, dart for safety - there's no safety in a ball, they can't hear/see danger coming & they can't dart away to a safe spot if danger does happen to come near them. Again, from a purely behavioural viewpoint, a ball is just not suitable for a chinchilla & I do wonder how much undue stress is put on a chinchilla placed into a ball for exercise.
Comments/discussion?