The most likely source for the assumption: Straight staircases running against defensive castle walls have intentional design rule where those going up have

The most likely source for the assumption: Straight staircases running against defensive castle walls have intentional design rule where those going up have right hand against the wall. Right handed defender can hack downward freely. They can also have intentionally uneven step length that makes running the stairs difficult. Similar rule is not as useful inside the castle or tower but, it might have been still used from time to time.