It's a really good explanation. Castle sieges were big events, so historically we know the outcomes. Nearly 100% of the time, the garrison has already surrendered if it's this bad. Medieval sieges come in three major flavors: ones where you sneak in, ones where you bombard the fortification, and ones where you don't let anything in or out and you wait until they give up.
If you examine a military you will find volumes of plans for incredibly unlikely situations. Once you have addressed all the likely and significant threats, you don't just stop planning--at least not any good military.
Saying that castle sieges didn't tend to involve stairway fights doesn't imply that stairways wouldn't have had defensive measures built in. That is post-hoc rationalization.
