I believe the Internet Archive is much less clear in this regard than public search engines. IA doesn't even have a clear takedown policy and no webmaster tools in place to give owners control on the archived content. Their crowler does obey to robots.txt rules but if you want content to be removed permanently you have to ask politely by email and in my experience they simply block the site urls from being searched but they don't make clear at all if content was actually removed from their servers.