Great points. Moderation is a very hard job, and good moderators understand they will likely be biased and can admit to it. I think moderation fairness problem is equivalent to the "auditing the auditor" problem; for some given events, how do we ensure that the labels given to the event are accurate and unbiased.
One solution might be for n moderators to evaluate and give the label to the reported violation, and ensure n is odd and larger than 1. However, this is tedious (although that is the tradeoff for fairness) and assumes there's an equivalent number of moderators who lean liberal, conservative, and neutral (in addition to assuming there's no biases created by the culture of the social media platform and management).
Perhaps each report should be given a detailed criteria as to why it was labelled as inappropriate, but this too would be subject to bias, emotional response from both parties, and slow down the moderation process which is likely backed up with many events in the queue, without really any direct benefit to the bottom line of the company although one could view this as a quality issue and lack of QA will ultimately produce an inferior product that is heavily QA'd.