Because that is the entire purpose of a contract: the private ordering of business between individuals. You can write a sales and shipping contract allocating risk to pass when/wherever you please. Risk can pass to buyer when the goods (horse) are still on seller’s property if that’s what the parties agree to. Risk can pass to buyer at some time after the goods are in buyers possession, if that’s what the parties agree to. Risk can pass at any number of points in between those two (when cleared for export; origin port; in transit; destination port; customs; etc.). Incoterms exist for so many points of risk transfer that there are charts to keep track.
The end of their responsibility is when the two parties agree it is. Neither party has control during shipping yet one party bears the risk always - that’s fundamentals of international trade.
A seller who agreed to such a contract would likely build that risk into the price of the goods (horse) to reflect the estimated number of times she would end up absorbing those costs. She would refine that estimate based on experience over the years she is in business IF she decided to agree to such terms.
One party bears the risk of loss at each point in the transaction. Where that risk passes from seller to buyer is completely up to the two parties and there is nothing unusual or outrageous about any of the choices, including the one AD’s sister agreed with her seller.