If one person broke into the technology for one plane, they could concievebly crash all the planes in the air, all at once before anyone knew it had gone turbo.
I've been thinking about this, and there's no way I'd get on a plane that could be taken over from the ground, it's far too easy to hack any system, especially considering the kind of software in play will be old but trusted, not the latest patch level.
However, the autopilots these days (well for the past 20+ years) are good enough to take off, fly to airport X and land itself, so what's to stop the plane saying "hey, I'm gonna hit a mountain/building in NY, let's not do that!". Sure there may be times when a plane actually needs to make an emergency landing, but a system where the pilots can only overide the autopilot's safety measures with approval/authentication from ground control could be implemented easily with no risk of being able to take over the plane from the ground. Maybe with a backup of if ground control is out of contact then both pilots must enter a personal code to overide.
I'm not sure how often autopilots fail, if at all, but if that's an issue then having 3 autopilots with a matching system (pilot A & B agree, C disagrees, go with A+B ) could be an option, albeit at a cost.