In this paper, we propose an integral data rectification strategy for phasor measurement units (PMUs) in multi-area power systems, comprising local data processing and central data recovery modules. The local data processing is designed for the purpose of detecting and eliminating false PMU measurements, which is performed in a decentralized manner, based on our previously developed dynamic state estimation technique; whereas the data recovery is performed in a centralized manner at the control center, based on a newly proposed adaptive-phasor approach. The recovered PMU measurements are then utilized in a low-frequency oscillation damping enhancement scheme, which is achieved by a modified proportional-integral (PI) power system stabilizer (PSS) mechanism embedded in the automatic voltage regulator structure of a synchronous generator. Control parameters of the PI-PSS are optimized by maximizing the critical damping ratio of the power system. This paper is intended to make a contribution to the need of high-quality data transmission in modern power grids with contemporary measuring technologies.