The invalid inference to make about the excerpt is:
People found it important to give the mentally insane a safe place to live.
While the excerpt discusses the actions surrounding Nellie Bly's commitment and the perceptions of those deemed insane, it does not indicate that there was a general consensus or importance placed on providing a safe place for the mentally ill. The focus is more on the ease of declaring someone insane and the institutional response rather than the care or safety of individuals in such facilities.