Well, on most aircraft there is a three-axis accelerometer that is a dedicated part of the flight data recording system. I think on Airbii, the recorded acceleration might be the same data source used by the flight control system.
A hard landing can be defined several ways ... vertical load factor at touchdown, which can be subject to aliasing due to a slow acquisition rate (relative to the near-impluse loading of a brusque landing) or vertical speed close to touchdown, which has is own problems because of ground effect on the pitot-static system if IVV isn't available or if there is varying terrain short of the threshold (trying the RALT rate).
There is also a whole host of contributing factors that could be examined for correlation ... was the approach flown particularly far from Vapp, was it a navy-style landing, did the landing balloon, was the descent gradient steep, etc?
Ultimately, you're probably going to be diappointed if you rely on any one data source (including crew reporting) to accomplish the goal of avoiding unwarranted maintenance time for inspections or flying around with a damaged aircraft