Firstly, this internet isn't going to be connected to the systems that drive your car. The worst that happens is you loose your music or someone screws with your GPS navigation.
Secondly, cars are already heavily computerized. There was the Toyota breaking problem which was fairly bad, but I haven't heard of any other issues. Cars are already very complex systems, they have 'bugs' of their own the breaking issue was a computer one but it could have just been normal mechanical failure, there is no data to say that a computer system running things is somehow worse. The idea is mainly caused by people dealing with BSODs on Windows and such. The stuff you use on your desktop is not the same stuff as is in cars. Cars will have very fixed functions for the software they use not general use like we see on normal computer. Computers see widespread use in planes, space shuttles without issues, occasionally there are problems but its no more of an issue than regular problems. Adding a computer if its done right it can help reduce the problems or their impact (such as a system that uses sensors to warn if something is running how or vibrating weirdly or one that makes an emergency call when a collision is detected and feeds live video to the emergency workers so they can asses the situation in advance).
I agree that this system seems to be a giant hand out, they are talking about money through the entire piece, nothing about how the end users can benefit. Will I be able to download music from my home system? Or will I be forced to purchase through the Toyota Music Store. What about apps, will we see a Apple type store or a Android free market?