Parity in Veterans Health Care Rights Act This bill expands eligibility for Department of Veterans Affairs (VA) benefits (including dependency and indemnity compensation) in situations where a veteran has been disabled or died as a result of medical treatment or vocational rehabilitation. Under the bill, the VA must award such benefits if a disability or death of a veteran was caused by hospital care, a medical service, or an extended care service furnished by a non-VA provider as part of the Veterans Community Care Program. The proximate cause of the disability or death in these situations must have been (1) carelessness, negligence, lack of proper skill, error in judgment, or a similar instance of fault on the part of the provider; or (2) an event that was not reasonably foreseeable.