To help those out who continue to have issues with this explicitly stated service, we've contacted Microsoft PR to ask what recourse customers have who are not being offered coffins. We will update as soon as we receive a response. We've placed the policy after the break for reference.
Taken directly from the Xbox 360 console repair FAQ:
What are the options for shipping my console to Microsoft?
You have two shipment options when requesting a repair online from Microsoft.
You can select the e-Label option for shipment. With this option, you provide your own box, and you can print out the pre-paid shipment label online. After you've packed your console for shipment, simply affix the e-Label you've printed and drop off the box with UPS. This option is more convenient, as you do not need to wait for a box delivered, and will often reduce time you are without your console. You should be sure to download the shipping label from the UPS web site within 10 days of receiving the email, or the shipping label will be automatically cancelled.
You can also select a box shipment in which case Microsoft will send a box to your home with a pre-printed shipping label affixed. You simply pack your console in the box and ship it back to Microsoft via our courier.