The final authority for assessing whether a heavy landing has occurred rests with the crew (certainly listed in Boeing MMs), irrespective of what other methods have been used to determine the condition. The G-Limit varies with aircraft type, e.g approx 1.9 for 757, and approx 2.1 for 737.
However, due to the sampling rates a condition could be missed or seen as a lesser event, hence Boeing prioritise the crew report as the final authority. (For those of you who are pilots and have had a hard landing and are scratching around looking at the ACMS for a G figure, you probably should be filling in an ASR and calling for maintenance!). The Boeing Phase I heavy landing check almost always is quick and easy, and for the 737, is usually as far as it goes as it is quite a tough plane.