This sounds reassuring. Was the first box damaged when you received it? Should we sign for our computer if the box is damaged?
My box had a very slight puncture in the side, but I don't believe shipping caused my issue. Admittedly, I'm not 100% sure on that. Also, the replacement box came in with a corner crumpled in.
These units are packed very well. If the overall condition is ok, I would sign for it and let AppleCare handle anything that's wrong with it.