Final answer:
Medicare does provide coverage for mammography screening costs, which means that statement A) is false.
Step-by-step explanation:
Out of the given statements, the false statement regarding breast cancer and older women is A) Medicare does not reimburse mammography screening costs. Medicare does provide coverage for mammography screening, which is an important tool in the early detection of breast cancer. It is recommended for women aged 50 and older to undergo annual mammograms for early detection and treatment.