UNLESS OTHERWISE AGREED TO the burden is on the seller to see that the item is safely delivered to the buyer. But, the buyer and seller can agree to any terms that they want to.

As a seller, you can specify that insurance is optional and that you will not be responsible if the buyer does not purchase insurance. When this happens, the burden is on the buyer and not the seller.

It seems that in this case nothing was agreed to about insurance. If that is so, the burden is on the seller.