(I want to echo some of what @Mad Scientist said.)
I wanted to point out that "A theory of Moderation" actually states that
As a moderator, your actions now represent the community, so you will
be held to a higher standard of behavior. You are an ambassador of
trust, with the same sorts of rights that the official development
team and community coordinators have.
I hope that all the moderators we have here agree with this ...
I think the situation is comparable to how with view people in law enforcement and judges. Here everyone has to obey the same laws. The police are not above the law, but since they are enforcing it, people for good reasons get upset when they do break the law. If you get a speeding ticket from a police officer who then him/herself breaks the speeding limits when he/she drives home from work, then of course it is going to seem unfair.
I think the key issue in this whole situation is that we give power to moderators and police officers. Police officers have the power to take your personal freedom away by detaining you. And when they have this power, it should come with serious responsibilities. The misuse of power should be punished.
Also, who arrests the police officer who violates the law? The police does. Who moderates the moderators? The moderators do. And it is not uncommon that the police will attempt to protect one of its own when charges of abuse are brought forth.
All this underlines how big a responsibility the moderator has. It is extremely important, in my opinion, that the moderator has the support of the community just as it is important that a community trusts and supports its law enforcement officers. When a moderator makes what is a degrading comment, then they should be aware that this might hit harder than when if another user had made the same comment. Why do we have this meta question? Because it is about a moderator.
What happens when a person in power breaks the law (that is the same for everyone) is that that trust is diminished.
So it is not a question of holding moderators to a higher standard in the sense of them having to obey stricter laws. But they should certainly know that their comments and actions will be scrutinized more so than the average user. And so in that sense, I think it that a higher standard is imposed on the moderators implicitly.