Bingo. Had to uncheck "show network," reboot, and it was gone from all Finder views. I also learned it's called the SIDEbar, not the toolbar.
Quizzical questions from the PC side:
1. Why did dragging off into space (desktop) work only for the foreground instance, and why was it fugitive?
2. Why did dragging the sidebar item to the trash not work at all (CMD-R brought it back)?
3. Why is the moon made of green cheese, and likewise all o-o software problems?
You don't have to answer #3.