As it stands right now, for a GroupSetting:non-moderated group, where Attachments are set to Moderate, but the person (user or admin) is set to Override: Not Moderated (P), the moderate-attachments setting takes precedence and the message goes into pending.
The manual doesn't clearly state what should happen or happens in this case.
In https://groups.io/helpcenter/ownersmanual/1/managing-members/moderating-individual-members there is no explicit mention: Override: not moderated: No messages posted by this member are moderated, regardless of the group’s or an individual topic’s moderation setting.
Conversely, in https://groups.io/helpcenter/ownersmanual/1/customizing-group-settings/message-formatting-settings there is some mention but still not quite clear: Attachments-Moderate: The system flags messages that include attachments for moderation (regardless of other moderation settings set for the group). It does mention group mod settings but not (explicitly) individual mod settings.
So it's not quite clear in this case what should happen, so is this precedence the way it should happen, or should the individual posting setting take precedence?
Regardless, those two manual sections can use a bit more clarification about this.