That rule applies specifically to the Creative Corner works and for use of images within posts in the RP forums (where you should preferably be using words to describe your characters rather than cheaping out by using art - especially when it's not your art or your character design. That's tantamount to stealing right there). Avatars are a separate system and there is no rule in place about using avatars that were found on an image search, and that is indeed common practice on the internet - including here.
So no, we generally don't target avatars unless they're actually inappropriate. Keep in mind when choosing an avatar image that some artists out there would not approve of their art being used by random people without their permission - and doing so anyway against their wishes would be thoughtless at best and disrespectful at worst. However - unless they contact us and specifically ask for removal of avatars that infringe upon their copyrights - That's up to the user's sense of decency and willingness to check out the original artist's guidelines for use of their work.
So no, we generally don't target avatars unless they're actually inappropriate. Keep in mind when choosing an avatar image that some artists out there would not approve of their art being used by random people without their permission - and doing so anyway against their wishes would be thoughtless at best and disrespectful at worst. However - unless they contact us and specifically ask for removal of avatars that infringe upon their copyrights - That's up to the user's sense of decency and willingness to check out the original artist's guidelines for use of their work.