That portion of any allowance payable because of the death or retirement of any member of the fire department which is provided by contributions of the City and County, shall be reduced in the manner fixed by the Board of Supervisors, by the amount of any benefits other than medical benefits, payable by the City and County to or on account of such person, under any workers' compensation law or any other general law and because of the injury or illness resulting in said death or retirement. Such portion which is paid because of death or retirement which resulted from injury received in or illness caused by performance of duty, shall be considered as in lieu of all benefits, other than medical benefits, payable to or on account of such person under such law and shall be in satisfaction and discharge of the obligation of the City and County to pay such benefits.