If you're shipping it air (overnight/2-day), they provide you with some box options at no cost other than the very high rate. If you're shipping it ground, you'll need to either BYOB or pay for one when you get there.
If you're shipping something other than a game that's rather heavy/bulky, try FedEx ground and bring it already packed in your own box, you'll more than likely get the best rate there.
Technically, though, your friend is wrong. It won't be cheaper to ship, you just won't have to pay for a box when you get there, and if it's not packed up, they can charge you for packing it as well.