No offence, but I think that dealer is full of it. The GM Fleet Order Guide is my go-to for info on constraints. Pick the model, then go to Distribution Updates, and you can get a list of weekly changes to the order guide. There are no mentions of NHT availability changes for the Silverado OR Sierra with LZ0. Also, if you navigate to the Mechanical section and find the NHT Package it explicitly states it IS available with the LZ0.
In my experience, GM keeps this documentation up to date, with weekly changes if required.
