Based on the evidence from the article "Nelly Bly Went Undercover to Expose Abuse of the Mentally Ill," the idea that is most likely supported is:
Psychiatrists knew their secrets were being exposed and were trying to do damage control to repair their image.
This conclusion can be drawn if the text discusses actions taken by psychiatrists to hide the truth about their practices or attempts they made to mitigate the fallout from Nelly Bly's exposé. If the article describes any measures taken by the psychiatric community to protect their reputation after Bly's revelations, this would support the idea that they were aware of the exposure and attempted to manage the situation.