I have not heard of anyone having trouble with a water leak on new truck. If the head liner is dry is it coming in around the door? If so I had a water leak on my 01 it was a simple fix and may apply here. The dealer had to readjust the door, they put the window down and then bent the top flange inwards to tighten up the gap on the weather seal. They also had to readjust the way the door was sitting on the mounting bolts, just loosen them up and then wiggle the door around and got a tight fit. But with your truck being 1 day old the dealer should have no issues with dealing with this.
I hope this is the only problem you have. Its a bumer with a new truck, good luck.