Here's why there was really an XBox 360 Shortage. (via Kotaku)
It looks like someone may have figured out what happened to a batch of those early Xbox 360s to make them lock-up and overheat. A German modder took apart two Xbox 360s and found that during assembly someone forgot to remove the protective layer of foil from the GPU heatsink’s heat transfer pad.
In other words instead of cooling, the heatsink was likely acting like a frying pan.
That matches up with the report received by Kotaku shortly after launch that a huge batch of Xbox 360s were recalled internally. In other words, they found something wrong and never shipped them out to stores, and a global shortage happened.