What SK posted about independent 3rd parties collecting data and what I posted about statisiticians cross checking the data of others are not mutually exclusive.
We are talking about all kinds of data and stats here. Most of the standard stats are pretty straight forward and easily double checked by simply reviewing the game, ie. batting average, OBP, Ks.
The data collected by pitch/FX is extremely accurate. It is recorded by 2 or 3 cameras (not radar guns) in each stadium. The cameras are equipped with very sophisticated software that tracks the pitch from release point until it hits the catcher's mitt. Pitch/FX revolutionized the world of pitching data, most notably the pitch framing stats.
BIS and STATS INC are two major baseball data collecting third parties. BIS is the one that supplies the data for UZR and plus/minus. There are several other lesser known such third parties that collect their own data, and I'm sure many MLB teams have their own team of data collectors. If one company posts some data that seems out of line with another companies, it will not go unnoticed.
Additonally, within any particular third party, they have taken every measure possible to cross check their own data and to eliminate bias and human error. For instance, BIS has at minumum two highly trained video scouts independently watching and charting every play. If their data does not match on any particular play, then additional scouts will review said play. They also rotate their scouts regularly, so that any scout is not always charting the same team or even the same division. This helps avoid biases.
Even with all the steps taken to eliminate human error, it will never be 100% eliminated. It can't be. BIS readily acknowledges where its shortcomings lie (with catcher defense, for instance) and these statisticians are constantly reviewing data and finding ways to improve upon it. The company's sole purpose is collecting, reviewing, and analyzing data in an effort to better understand baseball. A big part of that is testing the reliability of their data, which they also do constantly.
So yes, I feel very confident about the integrity and the consistency of the data collection process. Certainly, I would say it's, by far, much better than the home team's biased official scorekeeper's ruling on whether something is a hit or an error. For that matter, it's even, by far, much better than an umpire's ruling on whether a pitch is a ball or a strike.