"This should infuriate the informed investor because it
  means that Apple is quite literally trading on P/E ratios
  that do not reflect more than half of its business."

Yawn. No, it should -excite- informed investors because there's a tremendous opportunity to buy really cheap Apple stock from uninformed investors who don't know Apple's true earnings.

Unless, of course, the world economy collapses and demand for expensive consumer goods dries up.

Yeah - Apple at a PE of 7 (when you net out the cash) is an amazing buy - assuming the economy doesn't collapse completely.

Thats a significant success by any measure, especially considering its in billions of dollars.