They're not aging at an accelerated rate, they're exhibiting similar symptoms of aging from their microgravity environment (weak muscles, frail bones) and from there being no shielding from cosmic rays (cataracts).
Perhaps we could conclude that cosmic rays cause increased rate of aging. Actually, it seems pretty obvious really, that a body healing itself from radiation damage would "age" more quickly. Doesn't every cell division increase the cost of further cell divisions through mutations? And isn't there actually a mechanism to ultimately shut down cell division i.e. Telomere breakdown?
The linked article does a good job of refuting this hypothesis. There are radiation workers on Earth who receive regular, higher doses than what astronauts receive, and are not subject to these effects. It really is the weightlessness doing it, not the slightly higher ambient radiation.
Cosmic rays have enough energy to travel through the atmosphere and damage the sight of commercial pilots. Its not a leap to think that the exposure is significantly higher in orbit.
While the quantity might be just a higher, cosmic ray can arrive with more energy than particle accelerator can produce. I can imagine our bodies might not be able to handle healing from those types of events.
If you take any complex system out of the environment it evolved to survive in, it won't work as well. Doesn't matter which knob you tweak, it won't be the environment it evolved in. There will just be a different set of failures.
Is this necessarily true? I can see how it would often be true, in general, but don't see how it's necessary. For example, animals in captivity can often live longer. Lifespan and quality of life are decent enough proxies for "working well".
I would assume that stronger gravity would just come along with a different set of health issues (joint and muscle problems dealing with more stress, heart would be affected having to work harder to pump blood, etc).
I seem to remember from anatomy and physiology that most body cells don't really divide, the exception being epithelial cells, which are constantly being produced and shedding. So I'm not sure that DNA damage would tend to get propagated by cell division, at least in adults.