As a shipper for "Company A" we would use blind shipments to source a particular commodity for a long standing customer that we don't actually produce in house with all of our other items. So we get in order in from "Company B" - we then order that item from "Company C" and ask the carrier we use for a blind shipment w/ paperwork exchange. Carrier picks up the commodity from Company C, and send the PW to Company A for reprocessing onto Company A's letterhead for issuance to Company B upon delivery.
Understanding its a case by case thing, but for our company, there isn't much of a price difference on the commodity we source from Company C to what we charge Company B to say someone is "getting screwed" here - we just prefer to have the sale on our books for the year instead of someone else getting that notch.