"Fell down the stairs" is sometimes used for hiding fighting, bullying or domestic violence, but as for Kuina's case, she probably fell down the stairs literally. (Still controversial among Japanese fans, though)
Here's a quote from a sub reddit that's called 'askajapanese'. Someone asked the exact question about a person in a certain anime. In case you're more Japanese than this guy (or the others there) I'll believe you. Couldn't find a confirmation for that idiom.