Again, in my airline and I'm sure a it's the same in many, an overweight landing requires an inspection regardless of the descent rate. Otherwise a crew can simply state that the descent rate was within limits. If you were running an airline, would you be happy with that policy?
We also do not allow a crew to report a 'firm' landing or a 'suspected hard landing'. This is on the basis that it is either a hard landing or it is not. After the crew report the incident it is then up to the QAR captured data to determine if they were correct or not.