This isn't Timmy from accounting splitting off from Apple. This is the iPad division splitting off from Apple. If I'm holding Apple stock, I sure as hell expect to end up holding iPad stock in the event of a split.
Okay let's bring this metaphor back around. This is the iPad division quitting and issuing 'iPad' stock to all current owners of Apple stock. But your broker, who is holding your Apple stock on your behalf, is preventing you from collecting your new iPad stock.
If the iPad division quit en masse, formed a new corporation, and gave out free stock to people who could prove ownership of AAPL shares; E-TRADE has no obligation to do extra work with iPad Corp to make this possible…