We should be fair to everyone. But there's no contradiction - you can be fair to someone, and still judge them very harshly.
Disclaimer: I'm not a native speaker, feel free to correct me if I'm misinterpreting something.
An illustrative example where the use of the phrase "to be fair" would be justified:
Person A: "Brian has been very rude to me lately!"
Person B: "To be fair, he's been in a lot of pain since the surgery."
However, in this case originally, GP's request for fairness read to me as a pre-emptive dismissal of concerns regarding the ceo's performance, given that the examples did not address any criticism.
When I say I have no interest in being fair to the ceo of Mozilla, it's not to say that I believe they should be treated unjustly. Rather, it's that I believe their behaviour to be inexcusable given the context. Admittedly, this does veer a little from the dictionary definition.