I offer an audio recap of Martin's post here, with some additional notes below.
When reviewing the take-down request, the moderator has to consider several questions:
Does the post violate the community's publicly stated terms of use/community standards, whether through inappropriate language, personal attacks on other members, etc.? If so, the decision to remove the content is a no-brainer.
Does the content include content that is merely controversial? If it does, the moderator may try to convince the remorseful poster that the content should stay. (Sometimes, controversy is a good thing).
Have other community members already added comments to the original post If yes, and depending on the community software, removing the first post may also mean taking down all of the subsequent comments. That can cause a whole separate set of problems
Ultimately, the decision to remove content from an online community can be a nuanced one and often requires the moderator to weigh the request of a single user against the best interests of all the members.
In laying out his thought process, Martin's post serves as a good reminder that human moderators play an essential role in online communities.