You're right, it might still be possible. If that basket does have the original box, it probably would need additional packing material around it to prevent it from being damaged in standard shipping. I have an account with FedEx and that has made things easier many times for shipping odd items. It's much easier for a seller to just drop the item off with the buyer's name and account number and FedEx will pack and ship without any hassle for the seller.
When we've shipped vacuums, washer parts, etc. around the country the FedEx account is very helpful for that as well. The downside is that it makes "Yes, I want that!" way too easy and then you end up with a houseful of ______. LOL