A workaround and a clarification:

Workaround: Change Windows shortcut "Start in" to your jEdit backup directory such as C:\Backup\jEdit so the #untitled-1# file is created there rather than C:\Program Files\jEdit.

Clarification: Logging in as an administrator is not all the user has to do. They also have run the program with elevated rights ("as administrator) so jEdit is able to write into Program Files, an OS protected directory. This is unacceptable, in my opinion.

jEdit is clearly misbehaving by attempting to write files into the C:\Program Files directory and should instead write the auto save files into the backup directory.