tberg, I feel your pain. Your example is a bit more complex than Steve's. Steve's building is a storage building constructed when the area was considered agricultural. These sort of buildings were constructed often this way. Still doesn't make if right. As such he has plenty of land making setbacks not his problem. I think Steve has the tools now to proceed with his goals.
In your case this is a residence. I don't know all the details but if the illegal construction created any sort of a potential safety hazard such as being closer than 10' away from your neighbor then I can see why the city would not be pleased and unwilling to grant a variance for setback.
Keep in mind that there is no such thing as a variance for a building code violation only for local zoning and planning codes as long as they don't conflict with the building code. I know lots of bureaucracy.......