Pretty sure this myth was made up by One Piece fans who believe Kuina killed herself and you can't trace any unrelated Japanese source mentioning it.
I don't need to
You think a Shonen Author would say or be allowed to say that an 11 Year Old Girl committed Suicide because of Inferiority Complex?
Ofc he can't say it directly, it might influence Kids the wrong way, especially Japan where Suicide is considered a Major Social Problem.
So instead he had to say "She fell off the stairs", so that Young Readers don't assume she committed Suicide, but after they grow up, revisiting that Scene & what she said the Night before her Death & how Zoro reacted to the News & blamed her for leaving like that, will make them realize that she indeed committed Suicide. (Especially in a Manga where even Bombs might not kill anyone)
Suicide is a serious issue in Japan, they don't talk about it casually in front of Kids, so if they are forced to talk about it, they might try to use a different term/expression so the Kids don't notice & only Grown Ups do. So yeah, you won't find a Source for it, cuz it's not something Cultural, it's just logical normal behavior in front of Kids.