No group has a priority over any other. It's related to the up and down arrows next to the permission name. Permissions are cumulative. When you see the up arrow it means the highest permission has priority. When you see the down arrow, the lowest permission has priority.
High permissions are where the higher is better and a bonus for the user/group. Larger attachment sizes, more attachments, etc.
Lower permissions are where a lower permissions is better. Minimum time between posts, being required to view the ad island, having your posts moderated.
So in this case it looks through all of the groups that user belongs to. If it finds a 0 for post moderation in any of their groups, that is going to get applied.
Not to complicate matters more, but this is one case where the -1 permission doesn't work. For high based permissions, if you don't want the group to get that permission no matter what group they belong to, you can put a -1 in the permission for that group. When a -1 is encountered, they don't get the permission period. This obviously doesn't work with low based permissions, since forcing them to not get the permission just means their post still won't be moderated.
In this case, the only way you're going to get this group to have their posts moderated, when they belong to other groups that do not have their posts moderated is remove them from those extra groups. Probably have to make a new group, that gives the same permissions as the other two (hidden forums, engine room), but setting the posts to be moderated.
