You scale the walls, then go down in the actual castle. Why bother about the getting in the higher parts of the tower itself? People trapped inside a single tower won't last long, as they probably don't have much supply stored there.
The tight spiral staircase thing is about towers. The road toward and from wall was large non-spiral staircase. There is entrance from tower too, but in castles I have seen it was not the only way to get there.
