Have you tried it or is this an assumption on your part?
I haven't tried sending my Apple Thunderbolt Display in for AppleCare repair using the shipping option, but when I've used the mail-in option for phones, Watch, and iPad for AppleCare repair/replacement (including battery replacement!), they SHIP a box to you. Then, you place your item in their box and you can either call for courier pickup or you can send it to an authorized shipment outlet. There are options.
And, in all the situations where I've used the shipment options, shipment is not something I pay for but is included in the AppleCare.