I never said anything about not showing it off or not letting other see you avatar.
My apologies Cuervo, I misunderstood you when you said
"when someone uploads a custom avatar it is only available to that user" I thought you meant visually.
I wonder, how often do avatars get "copied".
Well on the same board I think it would be pretty rare (although there is no reason why more than one user couldn't have the same stock avatar). I think you're problem would be from hot linking by users of "other" forums.