It has been suggested that you give the supplier a call and I agree. Even if the response is that the load starts out at 8 cords and that's just the way it is, then at least you know and you can then decide if that is acceptable to you.
Having never purchased firewood in any form, I cannot offer advice on what the norm is, but KSWoodsMan makes a good point in that chances are the load does start out as 8 cords (I am giving the supplier the benefit of the doubt and assuming that the overall measurements add up when the load is on the truck).
A cord of wood is 128 cu ft of stacked wood. However, if it comes in 8' or 16' lengths, then you will have more air as any bends in the logs will cause the stack to be looser. Once you process the wood into stove lengths, it stacks tighter, but that form of measurement may not be accepted by your supplier because he didn't sell you wood in stove length - he sold you wood in log length.
The rounds here are a lot smaller then many of you are used to as we have smaller wood up here. If I sell a cord of 16" rounds and the buyer splits and re-stacks it, it will measure up to more than a cord. Can I go back and get some of that wood back? No, because I sold him a cord of 16" rounds.
The solution to your problem depends on you and your supplier (different folks will have different ways of addressing the matter). Maybe you can ask for a slight reduction in price, maybe just the phone call will prompt the supplier to try and load straighter logs for you, or maybe what you'll hear is "that's just the way it is."
Personally, 5.5 - 6 processed cords from an 8 cord log length load would not sit well with me, but if that is the norm then I would have to live with it or haul my own firewood (which I do anyway).
.... reading back over my post, I am not sure how much this helped.
I do hope that you get a satisfactory (to you) response from your supplier and that you will post it up here.