For the raw data that was freely (as in gratis and libre) available already, several other research groups have taken their published methods for quality-control and duplicated their results for that data. For the data that was not freely available, there were some groups that purchased the data themselves (much of this data was always available for purchase) and reproduced and published results as well.
On top of that, there were other research groups that performed "quality-control and analysis" on completely different sets of data, and their results agree well with results published by others. Note that I said the results "agree well" with each other. They are not perfect matches, and where there are differences, subsequent research and analyses have yielded refined methods and results. Think of it as a large bootstrapping problem.
Now, you ask that how do we know that the analysis was done in a fair and objective manner in all places? Well, we could never be 100% sure until each and every single datapoint has been vetted and doing this is now easier than before (not that it was impossible to do before). However, analyses and research on the published datasets have not revealed any such tampering so far, therefore *I* am fairly confident that it didn't happen. If you are not convinced, then feel free to take these datasets and others and perform the analysis yourself. Just remember to publish your findings whether they are for good or naught.