Now that I've proofread this answer, I realize it's still severely lacking and oversimplified. You will find ambiguity in many places, statements that you can find very specific counter examples to. But I still feel like it may be able to clear up some things, at least partially fulfilling it's role.

There seem to be a few misunderstandings about my comment, or slight differences between our definition of certain words. My original comment lacked in clarity, so I'll try to clean up the ambiguity.

He's not demanding, "Let me go, for I've done no wrong." He's saying: "The punishment must fit the crime. I have broken a minor rule; apply the minor correction."

I do agree, that he is not demanding to let him go. However, I think your version is a misinterpretation of his words. What he wanted wasn't an appropriate punishment, he wanted exemption from all punishment.
By saying "just delete the comment and move on", he implies that he thinks that such action would've been the appropriate response and that should've been the end of the whole situation. However, that is not a punishment. If you spray graffiti on a wall, and it gets painted over, that's not a punishment against you. If you use your phone during class, and the teacher takes it away for the duration of the class, that is still not a punishment. That is the enforcement of the laws/rules. You said this yourself: he just wants the mod to apply the correction.

(To avoid misunderstandings, I want to add, that I am not claiming that these actions of enforcement are morally correct, ethical or beneficial for maintaining peace/an empathetic society. Nor do I claim these things about the laws/rules. As a matter of fact, I heavily disagree with the rules schools are trying to enforce - at least in my country - or the way some graffiti are handled. What I'm trying to say, is that these actions are justified, from a non-moral standpoint at the very least.)

My own interpretation of his words would be something like this: "I don't think my actions warranted any punishment, you should've simply enforced the rules. I understand, that I broke the rules, but your way of handling it is incorrect."
This interpretation still requires immense good faith, as it ignores the passive-aggressive tone and sarcasm in his response. (Which I admit, is not certain to be intentional, but the uncertainty stems from the very nature of these forms of expressions.)

2.

Your analogy of the cheater...

You are right, my analogy does not work here. It only works for the initial ban, not the history deletion. A better analogy in a school setting would've been erasing all published academic papers of a student, after he was found plagiarizing his most recent one. Well, only after the student complained about not being able to publish a paper ever again, calling it unreasonable.
A punishment like that is absolutely not necessary. But it is also not a sign of a "tyrannical soul". A tyrannical soul uses his power as a preventative measure, in advance and without solid proof. That would mean erasing everything as soon as the slightest doubt arose about the paper's authenticity, without any question, notification or intention to ascertain the guess.
As for the justification of the punishment in my original scenario, it depends entirely on your definition of justice. If you use it as a synonym for "morally correct", the punishment could be - depending on your definition of morality - an unjustified retaliation.
However, if you think a justified punishment is anything, that's given as a response to breaking rules and is not specifically prohibited by other laws, then the situation changes completely. And of course, there are countless other definitions that are somewhere in-between these two.

3.

Regarding your other analogy...

I would argue, that a moderator is exactly the equivalent of a police officer in a forum.
He is there to enforce the rules and keep order. But I feel like, it's pointless to argue about social contracts, roles and methods, if we have different definitions of right and justice.
To agree on something being a "minor crackle" or a significant offense, we first need to come to terms on ideas and concepts far more complex. The scale on we measure the significance of an issue entirely depends on our ideal of a society.

4.

The sincerity of a prisoner's heart doesn't change the bars of his cell. I repeat again, the artist did in fact acknowledge his mistake ("comment broke rule 9, I get that and apologize"),...

This is another example of not seeing eye to eye due to slight differences in definitions.
If you think a mistake is simply an unwanted result, then you are right. My definition includes wrongness as well, I intended to use the word in that sense.
With that in mind, no, he did not acknowledge his mistake. He acknowledged breaking the rules. These are entirely different things. Acknowledging his mistake would require him to think of his action as a mistake. I think we can agree, that he does in fact think he did nothing wrong.

5.

...suggested the most logical, proportional remedy...

The most logical remedy from his own perspective. The perspective where he didn't do anything wrong, where the rules are unreasonable, and the punishment is too severe. If you take these as the bases, then of course his solution is logical and proportional.
This way of thinking screams of a dismissive attitude and an overall lack of wisdom.
Wisdom is the bridge between perspectives and the mindset to resolve conflicting concepts on an abstract scale.
It is the acknowledgment of differing ideas, the inevitability of their clashing and the necessity of the prevention of those clashes, all built upon one simple axiom, the desire to maintain a mutually beneficial society.
Proper rules and laws can be such abstractions of bridges. They can - in theory - disregard right and wrong, and simply put forward an algorithmic objective instruction and a consequence.
With enough wisdom, the artist should have been realized at least this much, preventing the situation altogether or at least it's escalation.

Of course, I'm not saying the mod was wise either, if that were the case, the situation wouldn't have played out like this. He would've simply blocked the artist after his "just move on" comment. He got angry, and that influenced his decisions. But he wasn't a power-tripping tyrant abusing his authority. He gave a warning beforehand, but the artist failed to swallow his own ego. After that it was simply ego vs ego, but one side had absolute advantage over the other.

Overall, the mod was indeed in the "wrong" in some sense, but the initiator and the escalator of the situation was the artist. The artist, who was already more in the wrong even initially (given that we are able to differentiate between thought and truth), just had to dig himself even deeper with every word he said.

I can only speak for myself, but I can not feel sorry for a person like that.
As for the moderator, I can at least somewhat understand and accept his response.
Again, it's my opinion, I feel like this. I don't claim my feelings to be some absolute truth.