"... the engineering that goes in to a modern car is immense, but fundamentally it's not new."
Even more fundamentally, it is nothing to do with driving. The self-driving cars that people are working on at the moment have three parts: a car, dozens of sensors, and some software.
The first is a commodity. All the tech firms who are doing research in this area have simply bought a car and modified it. As and when they perfect their algorithms, they will either license the technology (perhaps just to the big auto manufacturers but perhaps more widely) or they will simply buy cars from the cheapest manufacturer and modify them. It's not like Google or Apple don't have cash piles that would help them get this sort of business going, or like there would be a shortage of investors willing to help.
The second is also a commodity but not a commodity currently made by car manufacturers. The likes of BMW are no better placed than the likes of Google in sourcing this stuff or fitting it to a vehicle.
The third is the subject of research and It Seems Quite Likely To Me that the companies that are best placed in *this* race are ones that specialise in doing clever things with algorithms. The last I heard, the auto industry's IT departments were trying to fiddle their emissions results whereas Google and Apple were taking on problems like machine translation, speech recognition and machine vision.
So, yeah, it's hard to know where the smart people are going to put their money.