NOT always true - all depends on the FOB point
FOB Origin - it is the buyer's responsibility the second it leaves the shipper
FOB Destination - The responsibility belongs to the seller until it hits the receiver's dock
I'm no lawyer, but I did take a business law class in college. From what I remember, it works like this:
If I purchase an item from you and I arrange for a shipper (UPS, Fedex, Yellow Freight, etc) to come pick it up from you and deliver it to me, then I have made a contract with the shipper who is my agent and shipping is then my responsibility. Once you deliver it to my agent (the shipper) and something goes wrong in shipping, that's between me and the shipper. You have fulfilled your part of our contract by delivering the item in good condition to my agent. Our transaction ends when I have paid you AND you have delivered to my agent (the shipper).
If you arrange shipping, then the shipper is your agent and shipping is your responsibility. You have a contract with the shipper and you have a contract with me. If something goes wrong in shipping, then that is your agent's responsibility. You have to work that out with them, but you still need to complete our transaction or refund my money. Our transaction does not end when you get your money and put the product on the truck. It ends when you get your money AND I get the product in condition as agreed.
Try this some time. Buy something with the seller arranging shipping (let's say UPS). It gets lost or damaged in shipping. Now call up UPS and try to make a claim. They will tell you to talk to the seller because you are not their customer. The seller is. They had a contract with the seller, not you. The seller paid them, not you. If there was insurance to be paid on that shipment, it goes to the seller, not you.