I agree: if there were some way to know the truth other than through the "filter" of personal observation, it could not be contradictory. However, in practice that doesn't happen very often.
Specifically, think about how we know about Apollo. We know about it through personal recollection, through photographs (which aren't as objective as you might think), through sound recordings, through telemetry, and through massive amounts of printed information. These are not perfectly transparent means of conveying fact.
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