Fundamentally, their case for being ahead of the pack rests on 5 pillars.
1. Lidar and high precision mapping doesn't really help towards a generalized solution to the problem. I think they are probably correct here.
2. They have a special purpose accelerator specifically designed for this problem, with redundancy built-in at every level, and the necessary performance for the task. This is a tossup for me, and mostly only matters from a power consumption perspective.
3. They are not trying to explicitly program rules, as this is an intractable problem. Instead, they want to interrogate the fleet to provide high-quality data so that the neural network can train itself. This again, seems like a sound principle to work on.
4. They have the infrastructure (i.e. the fleet + software) to gather high quality data to feed the network. Large volumes of similar data alone is not enough, as you run into the overfitting/sparse data problem. They've built out the software infrastructure to gather a diversity of high-quality examples so that the neural net can learn in a very generalised way.
5. Don't under-estimate exponentials.
The fourth and fifth are still the biggest stumbling blocks IMO. The number of bizarre cases are so many, it's not clear to what extent even that kind of infrastructure can gather sufficient data to solve the problem. However, one thing that is clear is that, at least, they do have no. 4, whereas the competition is not even close, which gives them a significant leg up. As for Elon's predictions on the timeline, he seems to be relying heavily on no. 5, but it's also not clear whether skynet is actually learning at a geometric rate, and to what extent no. 4 will scale to allow it. Considering the rate at which auto-pilot is reported to be improving, they are probably expecting a good outcome.