Import duties if fulfillment by seller

Just to be clear, I am not talking about FBA, but rather fulfillment by the seller. Let’s also assume the seller is based on a country other than the buyers’ or the registered Amazon marketplaces.

In this case, I’ve read around that the seller is responsible for paying import duties if the buyer is located in the same country as the marketplace where the item was bought from, such as an Australian resident buying from https://www.amazon.com.au/. However, the buyer would be responsible for import duties if he purchased the item from a different marketplace than his own, such as an Israeli buying from https://www.amazon.co.uk/. Since the price of import duties needs to be included on the item for covering costs, it seems that the Israeli buyer would essentially pay import duties twice – once for the UK, already included on the price of the product, and once for the Israeli customs. Is this indeed the case?

Furthermore, the seller would pay the import duties to the carrier, not to Amazon, is that correct?