In the video, when you opened the product editor – there was no stock information for the product. Also, when you opened the product page I could not see any information about the stock status either. That very likely means, that WooCommerce has no knowledge of the stock status of the external product, so it simply returns it is out of stock.
In order to have the stock status available, it must be requested from somewhere. These products are external so the external store handles the stock, which I guess is not connected via API or any other means to WooCommerce to report and to store the stock status locally.
Simply put, the reason the wrong stock status is shown, that this information is simply not available for the shop.