The nannies are very good at controlling the Z when someone pushes it a little too far but they are designed to ASSIST a reasonable driver and not make the world safe from a total moron. If you try to enter a hairpin turn on the Tail of the Dragon at 140 MPH you are past the point where anything can control the vehicle (well anything except the solid rock side of a mountain). If you accelerate a little too hot with cool tires on a cool surface it will get you back in line. But if you nail the throttle on cold tires on a crowded street you are likely to be into something before the control systems can unwind your stupidity. The torque from a Z06 will result in behavior you won't generally see with a naturally aspirated or even the typical turbocharged engine which won't have the near instantaneous availability of diesel engine like low RPM torque.

Remember, the slang term for these protective systems is "nanny" and not God. Like a children's nanny they help keep children in line but they can't always overcome a determinedly stupid adult.