Why did you not read the article I suggested earlier ( Robot Cars Can’t Count on Us in an Emergency ) It mentions for example data collected by Nauto, or Stanford research on how long it takes a human driver to regain control of the car, which is a the heart of the debate whether Level 2 can ever be safely implemented. Level 2 by the way requires the driver to regain control of the car at any time with little or even no warning at all (if AP is driving straight into a median divider, even if it doesn't warn you, you have to take over). This is the biggest problem with AP, it's the fact that it required the driver to babysit it at all times (and for those who don't, some get away with it, some pay for it).
That NY Times article focuses primarily on Google's efforts to test Level 5 cars and there is no data at all on Autopilot. Level 5 testing is a very different situation from Autopilot, where the driver is instructed to keep hands on wheel and maintain control of the vehicle at all times and there is nag system a nag system setup to help ensure compliance.
In fact, the NHTSA investigated this very issue and concluded that Tesla's instructions to drivers and nag system as part of its Autopilot report had addressed the issue of driver distraction to its satisfaction:
The potential for driver misuse was evaluated as part of Tesla’s design process and solutions were tested, validated, and incorporated into the wide release of the product. It appears that Tesla’s evaluation of driver misuse and its resulting actions addressed the unreasonable risk to safety that may be presented by such misuse. https://static.nhtsa.gov/odi/inv/2016/INCLA-PE16007-7876.PDF (page 10, section 5.3)
Bottom line: you seem to be arguing that it is impossible for Tesla or any other manufacturers who are developing Level 2 systems (GM, Audi, Nissan, Mercedes to name a few) to develop systems as safe or safer than average drivers.
But that's just a hypothesis that needs to be proven with data. The data analyzed and reported in the NHTSA study seems to be saying exactly the opposite for Autopilot. As more data comes out on all of these systems we will learn more, but so far Autopilot's ability to avoid accidents and save lives looks very promising IMO.