About 5 mins after food is burnt on the stove, if not removed, it will set the ship on fire. About 5 mins after that (on a sloop) the ship will sink.
EDIT (time for a little Sea of Science):
Having first tested this when fire was added to the game, I just re-ran this test and confirmed my timings are more or less accurate for a sloop. I put a splashtail on the stove. Ship caught fire almost exactly 5 mins after the food was burned and sloop sank 5:15 after that (there may be some RNG involved in how fire spreads and holes fill the ship with water).
To try to reproduce a scenario that would not cause fire, like in the OP, I then tried it with a very small amount of water in the hull from a collision grade 1 hole. This did not prevent a fire nor the spreading of fire.
Next, I tried it with a moderate amount of water, up to the quarter line on the barrels below deck. This prevented fire from being created (CoR experts will not be surprised there!), but time to find the minimum amount of water required right?
Using 3 buckets of sea water (for those who don't know, sea water fills a little differently to barrel/hull water when emptied into a ship). 3 buckets prevented a fire.
[Now, the one thing I hadn't thought about up to this point was that I was doing the tests after the last successful fire with an already burnt fish to speed up the testing... d'oh bad science! So, I re-ran with this fish again on a completely dry ship and confirmed it still caused a fire after 5 mins, so all good, no foul... phew!}
On with the bucket testing, and 2 buckets of sea water.... this prevented fire as well.
1 bucket of sea water: did not prevent fire.
So, to confirm the 2 buckets of sea water test, I re-ran with that amount. Even leaving it for 10 mins, there was no fire.
That leads me to believe one of 3 possible reasons for the events in the OP:
or
