No competent pilot would ever let a hard landing go unreported. After all it maybe his a$$ sitting in the left hand seat when the damage he caused, decides to make itself known.
Unfortunately, that is not always the case, for the reasons outlined
already (job fears etc), and not all aircraft are Airbus or Boeing
either.
In my last outfit ,one aircraft was grounded for 'heavy' landing checks
(ie over Max Landing Weight) some two weeks after the event when the JAR-OPS QA audit turned up a loadsheet discrepancy.
With regard to 'hard' landings (excess vertical speed at touchdown)
many of these events went away after a programme of regular DFDR d/loads was introduced.
In all cases, as said earlier, follow the AMM!!
ttfn