My issue was small and probably less complicated than others', but just to provide an update. I had a problem with a hotel I stayed at in December so they said they'd issue me a $30 customer-service credit, which would be refunded to me through Chase. After a couple of mostly unproductive follow-up calls to the UR people to confirm whether this in fact was the case and how long the credit might take, I ended up getting the credit to my card just a couple of weeks after my stay. That was a pleasant surprise, as I fully expected the refund to get lost in a black hole between the hotel and whatever Indian outsourcing firm is in charge of the rewards program.

Of course that was just a simple refund to the credit card - no airline miles or UR points or other faux currencies to track and account for.