Practically every plan document I've ever seen (I used to audit employee benefit plans) uses hours "worked" in the vesting requirements. Hours "paid" could be too easily manipulated due to various payroll frequencies (weekly, bi-weekly, semi-monthly, monthly). Regardless what your HR manager SAYS...the PLAN DOCUMENT IS the governing instrument and the vesting schedule shouldn't be that hard to interpret. It sounds like you don't want to make a scene or damage any relationships, but if your HR department won't abide by the plan document I'd advise you to pursue other sources to support your eligibility.
Worst case scenario: You may plan to stay employed there long enough to become fully vested but A LOT can happen in five years (I'm assuming that's the required time). It is surely worth it to you and/or your beneficiaries to get this fixed NOW.
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"The words you say never seem to live up to the ones inside your head." Chris Cornell (Soundgarden)