The option is located under "Administer Menus-->Settings-->File system settings".

When we enable that choice under "File system settings" options. Drupal does take control of the image links.

But the image links, when displayed, generate entries in the log like: "system/files denied access".
(Links like: http://www.sitebuddy.com/system/files?file=pictures/picture-1.jpg )
In other words, it appears that the display of the images is not permitted by default (i.e. "system/files denied access" in the log).

So without modifying some PHP code, it appears that to enable everyone to see image you have to use the option:
"Public - files are available using http directly"