Final answer:
Having a terminal illness does not make a person eligible for Medicare; eligibility is based on being 65 or older, having end-stage renal disease, or having other specific medical conditions.
Step-by-step explanation:
The criteria that would not make a person eligible to receive Medicare benefits is 'a person has a terminal illness'. Medicare is primarily available to people aged 65 and older, and it also provides coverage to those with certain medical conditions, including end-stage renal disease and individuals who are permanently disabled. However, having a terminal illness on its own does not make one eligible for Medicare unless one of the other criteria such as age or specific medical condition is met.