They probably mean they opened the box and it was empty (i.e. they got sent a parcel, and the item's box was inside the parcel, but the item itself wasn't in the box).
I've worked in quite a few eCommerce companies on the fulfilment side (although not Amazon, but including Amazon sellers) and this is pretty common - the overwhelming cause is that a scammer buys a product from an online store, takes it out of the box, replaces it with rocks or something of a similar size/shape to make it weigh the right amount, then shrink wraps it to make it look like it hasn't been sold and then returns it for the full value.
However sometimes customers also lie and say that they received an empty box, when they actually had the item inside.
It is very rare that the manufacturer will ship an empty box (however it does sometimes happen).
Because of this, most eCommerce companies adopt a policy of "If the 'new' item was previously an unopened return, allow the refund, however if not, do not allow a refund". eCommerce companies track this by using different bins for returned products (or at least by not returning that product to a bin with the same SKU that is non-returned). This sucks for the customer if you are one of the unlucky people that gets a box sent empty by the manufacturer, but fortunately that's very rare (it's a tough one to resolve without lots of theft, as it's very easy for people to say that the box was empty and very hard to prove otherwise).
This is even more difficult with third party sellers, as Amazon may not have full visibility with how they are tracking returns, and those third party sellers may have different policies around 'received empty' returns (I've not seen the above in any official policy, but can confirm it is common practice - again not with Amazon but I've worked with a number of eCommerce companies with similar issues and policies).