And how have we discovered the incorrect and dishonest claims?
Through the process. You never have to trust the data if you have a good process. Process will verify data. Process will verify sources. Process is impartial. Trust the process, not the results.
Also, I take issue with the attempt to conflate people who are incorrect with people who are dishonest.
There is nothing wrong with being wrong. Being wrong is the first step to being right. You can't be corrected if you're never willing to be wrong. And we can't learn if everyone has to wait to be completely correct before making a claim. Often, we don't even know we should be looking into something until someone makes a claim that turns out to be incorrect on further study.
Knowledge isn't furthered in "eureka" moments where we have all the answers at once, it's in observing something and thinking, "Huh, that's weird", then seeking the answers.