I have not had the bad experience recounted here, but I can see that part of the problem is that GM's logistics are stuck in the 20th century. Online retailers know exactly where every item is at all times, when it will show up, how many to stock, and how to respond to contingencies. If a DVD gets a favorable review, the factory is cranking out more copies by noon.
There is software that does an excellent job of putting optimum spare parts inventories at each depot and each service site. The airlines swear by it.
When Amazon misshipped a $15 book, they overnighted another copy to me. I'm not a VIP. That's the new normal for customer service. If the initial parts shipment does not get the car back to the customer, all other shipments should be overnight.
If GM can't fix their system quickly, they should outsource it to UPS. UPS offers end-to-end logistics to major companies on a "my warehouse or yours" basis.
Some years ago, GM and other US manufacturers thought that the only way to ship zero-defect cars was to spend unacceptable amounts on QAing the finished cars coming off the line. Honda showed them different. Now it's time for GM to learn from Amazon.