Braking systems are controlled by a dedicated embedded software system that's extremely well-understood and well-tested (probably even formally verified). All it does is check the ABS (and anti-skid) sensors and moderate the braking pressure to avoid locking the wheels. It also has a fail-safe system that gets rigorously tested, e.g. if a sensor fails. All possible values of all inputs are known, and the configurational space of those inputs is small enough that you can exhaustively test correctness.

It's plainly obvious that a braking system controller software is a very different beast from an autonomous car software, and I have no problem understanding why someone would trust th former and not the latter.