I have a 2014 LTZ with the 6.2 Liter and the 3.73 gears. I have the whistle noise and the rough idle in the morning. I have about 14K on the truck and last week the check engine light came on. I called on star and they ran a diagnostic check. I told them that it has taking a few extra cranks to start in the am, there is black smoke at a cold start up, and a rough idle in the morning. The rocket scientist came back and staring telling me about tire pressure and all the things that I do not care about. I asked her what codes were causing the check engine light to come on and her response was that I had a rough idle at start up. She said I have a week to bring it in.
My theory is that the DI fuel injectors are bleeding down. They flood the cylinders a bit which causes the black smoke and the rough idle. Once the truck is at operating temp, she runs like a champ. I just do not have the time to bring it in. My last truck had 100K on her, and I never had to bring it back to the dealer, not once. Just Oil changes in my driveway.