Pension and Budget Integrity Act of 2019 This bill prohibits certain provisions from being counted as an offset to determine budget points of order for legislation in the House of Representatives or the Senate. Specifically, a provision that increases or extends an increase of single-employer pension program premiums payable to the Pension Benefit Guaranty Corporation (PBGC) may not be counted as such an offset. (The PBGC is a federal agency that insures the benefits of private sector, defined benefit pension plans. The PBGC is financed by insurance premiums paid by sponsors of the plans, investment income, assets from pension plans taken over by the PBGC, and recoveries from the companies formerly responsible for the plans.)