I believe it is a pop culture connection. There is a classic horror movie in which the "bad or possessed" kid is named Damian and the characters draw that connection to it's similarities to demon. Thus because of the pop culture association that is how the false etymology took root.
Please rate my "Names I would Use" list & "Backup Favorites" list. Feel free to rate some of my other lists too if you have the time.
https://www.behindthename.com/pnl/223226/138473