It is not possible for an over-inflated, not calibrated automatic blood pressure cuff to cause rib fractures. However, rib fractures are commonly caused by a direct blow to the chest, often caused by a fall, or an accident. You can read more about it from http://www.webmd.com/a-to-z-guides/fractured-rib-topic-overview.
To much pressure on any bone can cause a fracture, I highly dought a bp cuff would do it as most have a air bypass valve. You can infact fracture a rib by a real hard string of coughs or a violent sneeze.