For some reason this situation doesn't fully pass the smell test.
1. In general Apple does not repair Cinema Displays in store. They tend to be a low volume store, and are very rare to see in a repair situation. Parts are not kept on hand, and training is not directed this way.
2. It would be very unusual for an Apple Store to choose to repair instead of returning an item that new - it also doesn't make sense to me why the OP wouldn't demand a new Display. No way I would take back that same Display with an issue that fast.
However, giving you the benefit of the doubt please know...
Individual stores have no way to control how fast parts arrive - in general it is fairly speedy (1 or 2 WORKING days), but if a part is back-ordered it can take additional time.
If I were you, I would make the request to return the previous model; if they give you any static ask to speak to a manager (you shouldn't even have to go this far).
I think I agree about the funny smell. If it was bought at an Apple store and brought back 3 days later, they would have given him a new one- without a fuss. If it was bought at Amazon it should have been handled through their customer service and they would have sent out a new one the same day before the bad one had even been received. If it was bought at Amazon, and then taken to an Apple store 3 days later, then the Apple store didn't really have any business offering a replacement and I'm surprised they even offered to fix it onsite (without parts) instead of ship it off for repair. The described customer service is terrible, but it is also a terrible (and unlikely) position for an Apple store to be in. They don't want to fill up their back room with big things like ACDs that are waiting to be fixed until parts come in.