I used the scroll to save the burning ship while standing outside of town, having circled the orc ship and thus happened across it (and got the 'we saved the ship' journal update), and could see the firefighting NPCs wander off along the docks as a result.
However, upon entering the town gate, a "Help, the ship's on fire!" NPC ran off toward the docks and the firefighting NPCs were back there, going through the animations and shouting about the fire... even though the ship wasn't burning at that point.
Seems like the quest script doesn't handle it well if you skip a stage.