No. Those two statements, they lose money shipping and they make money on volume, can both be true at the same time. It's an accounting thing, they're booking a certain amount of shipping revenue on each item they sell (even if shipping is "free") and they have certain costs associated with shipping. In this situation, what "they lose money on shipping" means is that the fraction of income which is booked as coming from shipping is less than the costs they incur doing that shipping. They're still net positive on selling shipped goods because the margin in other aspects is high enough that it covers the loss in shipping.
Companies do it this way to determine what parts of the business are doing well, and what parts need improvement. They might choose to improve profitability in shipping by making shipping cheaper in some way, or by changing the wrap they use from individual sales (thus reducing expected profit margins).
So yes, they lose money shipping. And yes, they make money selling things which are shipped.