but I'd like to be sure the claim was genuine - how can I do that?
When you can think of a way, please let us know.
Apart from the rare occasions when Royal Mail or a courier records that an item was damaged in transit, it's seldom possible to prove where damage occurred.
With eBay's simple delivery buyers are not even required to return the allgedly broken or not as described item. As you say, eBay seems willing to refund them with little or no evidence. But before simple delivery, eBay used to make the seller refund them with little or no evidence! So in this sense at least, sellers have benefited from simple delivery.