Ok, I know what he is talking about here. Stoping custom avatars will not solve this problem because all someone has to do it right click an image, view properties and there is the path. I doubt a hack can be designed to stop this because its more of a .htaccess issue. The correct term for this is called "Hot linking".
Using .htaccess, you can disallow hot linking on your server, so those attempting to link to an image on your site, for example, is shown either the door (a broken image), or the lion's mouth (another image of your choice, such as a "Barbara Streisand" picture- no emails please). There is just one small catch- unlike the rest of the .htaccess functionalities, disabling hot linking also requires that your server supports mod_rewrite. Inquire your web host regarding this.
With all the pieces in place, here's how to disable hot linking of images on your site. Simply add the below code to your .htaccess file, and upload the file either to your root directory, or a particular subdirectory to localize the effect to just one section of your site:
RewriteEngine on
RewriteCond %{HTTP_REFERER} !^$
RewriteCond %{HTTP_REFERER} !^http://(www.)?mydomain.com/.*$ [NC]
RewriteRule .(gif|jpg)$ - [F]
Be sure to replace "mydomain.com" with your own. The above code causes a broken image to be displayed when its hot linked.
If you're feeling bitter, you can set things up so an alternate image is displayed in place of the hot linked one. The code for this is:
RewriteEngine on
RewriteCond %{HTTP_REFERER} !^$
RewriteCond %{HTTP_REFERER} !^http://(www.)?mydomain.com/.*$ [NC]
RewriteRule .(gif|jpg)$
http://www.mydomain.com/nasty.gif [R,L]
Same deal- replace mydomain.com with your own, plus nasty.gif.