Turning 65 and gaining eligibility for Medicare doesn’t disqualify an employee from continuing to receive employer contributions or making their own contributions to an HSA. Only if one voluntarily enrolls in any part of Medicare would they then be disqualified.
Likewise, enrollment in Medicare for most, is not automatic when they turn 65. Only those who have contributed 40 quarters into Medicare when they receive Social Security benefits are they automatically enrolled in Medicare Part A; or those on disability are automatically enrolled after their 25th disability payment from Social Security.
Employees wanting to work a few more years and delay retirement are able to continue to reap the triple tax advantage benefit of an HSA if they are otherwise an eligible individual.