Back to My Mac Problem - “connected as: VNC”

Posting this because I could not find an answer elsewhere on the internets.  I had one computer that, when I tried to access its files via Back to My Mac, gave me a message, ”connected as: VNC” and showed me no files.  I could not authenticate as a user on that machine.  It turned out that I had not turned on File Sharing in the Sharing Preferences.  Once I did, all was resolved.