> The OS/process analogy doesn't hold here. The process has completely isolated state from the kernel.

In one direction. That's why I'm asking you if you reboot your machine when your kernel dereferences a wild pointer when executing a system call on behalf a process - in theory it could have corrupted the kernel itself or any process on the system, but Linux makes a practice of trying to just abort execution of the system call, kill the process, and keep going.