Statisticians do everything possible to eliminate human error and bias. They will never be able to be 100% free from error or bias, but implying that the data is corrupt is nonsense. First off, statisticians will readily admit when there is any kind of noise in their data. Secondly, they are frequently testing how reliable their data is and making improvements from it. If the data is not reliable, they typically don't publish or use it. And if one statistician or group publishes some data, you can be darn sure that it is being cross-checked and re-tested by other statisticians.
No stat is perfect, but seriously, the newer stats like UZR are very good, despite the flaws. UZR and +/- are head over heels better than fielding percentage or errors. I can also guarantee you, though I have no proof, that the stats are less biased than the scouts are.