Nope. Apple agrees to buy 1 to 5 million ipod screens from a supplier, at a $10 per screen (totally made-up figure). They say they want boxes of 100,000 units, delivered within 1 week of whenever they feel like asking for them. So Apple doesn't need a warehouse, they get their supplier to pay for that.
They also have an identical deal with another supplier, so they can play them off against each other if they need to renegotiate. Most companies would just go with whichever supplier was cheapest, but Apple may find it cheaper (in the long run) to keep the competition going.
The suppliers don't need that much of a warehouse, either. Let's assume that Apple is forecasting that 100,000 iPods per week will meet demand. They go to the supplier, and tell them that they need the screens delivered at 100,100 per week(assuming that a very high .1% of all screens are defective, after the supplier's QA). The supplier gets their factories producing around that number per week, and ships them out immediately. Apple takes them in, and immediately produces iPods with them, where they the go out to retail. This way, neither Apple nor the supplier need to keep more than a week's worth of stock.
The reason that Apple keeps a similar deal with another supplier is if anything goes wrong with the other company. So in the previous example, if in week 5, Fukushima happened, and the first company was unable to keep production up, Apple could go to the other supplier and keep up production, with a very short(maybe a couple of weeks) delay. This is vital, since Apple doesn't maintain that much inventory of new parts.
The other benefit to this setup is that it allows Apple to almost instantly double their supply inputs for new product releases or for the holiday season. If necessary, Apple can use both suppliers to get 200,000 screens per week, then just rent a few warehouses for the temporary storage of new products or the holiday rush inventory.
"So Apple doesn't need a warehouse, they get their supplier to pay for that."
That wouldn't make things cheaper since the cost of storage would simply be passed on to Apple by the manufacturer. The point being made is the supply chain has everything built just-in-time with minimal storage needs across the board.
Both Apple and the manufacturer wouldn't be storing much of anything. Everything is built in time to ship.
The other thing is just how many units Apple ships. They have to go with multiple suppliers at times just to have enough parts in the first place. You're talking about a company that buys a significant proportion of the world's NAND flash production a year ahead of time.
They also have an identical deal with another supplier, so they can play them off against each other if they need to renegotiate. Most companies would just go with whichever supplier was cheapest, but Apple may find it cheaper (in the long run) to keep the competition going.