Personally, I'd print this out
And read it, while you are at it to familiarize yourself with what happened to the car. The problem is 99% a failed upper intake, caused by the EGR gasses abusing the upper for years.
As well if you search the 92-99 mechanical section you will find post after post about how there is not usually an overheating issue when this occurs because of the speed in which it happens is usually very quick.
If necessary have the car towed to another dealer for another opinion. However they will need to pull the upper intake off the car to verify the problem. Nearly any GM dealer that sells a car with the 3800 in it should know of this issue.
For a little insight on how to handle a dealership that is giving you a hard time (and a laugh) find the post by Charliemax that is currently ongoing as his car has suffered the same issue.