Which client would be eligible for health insurance under the Medicare program?

The Medicare program primarily provides health insurance to individuals who are age 65 or older. While there are provisions for younger individuals with disabilities and certain conditions, the standard eligibility threshold is set at age 65. This age designation reflects the program's foundation on providing healthcare support to seniors, acknowledging both their increased healthcare needs and the transition into retirement age when employment-based health insurance may no longer be available.

Individuals who are 62 or older may not be eligible for Medicare just yet, as they haven't reached the requisite age threshold. Although those with disabilities may qualify for Medicare before they turn 65, the expression in the option focuses specifically on age. Lastly, while veterans have access to specific healthcare programs through the Veterans Affairs system, their veteran status does not directly influence eligibility for Medicare like the age criterion does. Therefore, the eligibility under the Medicare program is firmly rooted in the age of 65, making it the correct answer.