Mitzy,
The best policy with drywall is to keep it dry, lol.
If it got soaked once it should be okay. Drywall is actually bent around radius walls by thoroughly wetting it and then letting it dry in place (usually is 1/4" drywall but that is beside the point) so it isn't something that is not done. Would I allow for it to repeatedly soaked, no. Would I ask politely if it was all going to stay out for an extended period of time for my contractor to bring the rock in where it is going to stay dry, yes (drywall contractors usually get the rock up pretty quick upon it arriving on site so I am not sure how long your contractor intends for it to stay out). Do butt ends and factory sides of rock get cut off? yes how much and locations the cuts come off of depends on the job.
I am not sure if I would panic quite yet because the top piece that got wet may not even get used. But if the contractor is going to be leaving this rock exposed to the elements for some time I think I as the client would request he bring it in as this is not a good policy since this is a finish material and usually immediately after hanging the rock it is taped textured and painted in rapid succession I would opt for the rock to be dry.
I hope that this is not too vague and answers your questions. I am sure that you will receive opinions from other professionals on this site and this is simply my viewpoints.
Good luck, be safe!