The first automated aircraft would probably be data-linked to the ground with "pilots" monitoring several at once, able to step in and assume remote control if necessary. This would remove the "can it deal with any hypothetical situation?"
Can you imagine a guy on the ground, sipping his coffee, and being "handed " Sully's ship with both engines out, making the same decisions as Sully's?
Nup, the aircraft would be at 500ft AGL before he was beginning to understand the situation. He wouldn't be 'invested' enough.