Veterans' True Choice Act of 2023 This bill allows covered veterans to receive coverage under TRICARE Select, a health care program of the Department of Defense (DOD). Veterans covered by this bill include those with service-connected disabilities, former prisoners of war, Purple Heart recipients, Medal of Honor recipients, those discharged from service due to disability, and those entitled to disability compensation. The Department of Veterans Affairs (VA) must reimburse DOD's costs of enrolling eligible veteran beneficiaries in the program. A covered veteran may not concurrently receive hospital care or medical services from DOD and the VA.