The invalid inference to make about the excerpt is:
People found it important to give the mentally insane a safe place to live.
This statement cannot be inferred from the provided excerpt, as it does not mention the conditions or the intentions behind the establishment or treatment of the insane within the boarding house or the Bellevue Hospital. Instead, it focuses on how Bly was able to present herself as insane, reflecting more on societal perceptions than on the provision of safe living conditions for the mentally ill.