re: the 'Edit' section
'trustworthy' as a characteristic of a system, is still bound to some inconsistency OR incompleteness.
'incompleteness' is what people notice
'inconsistency' is what you have proposed (aka LYING)
Since humans lie to each other, we've developed techniques for sniffing [out lies].
so I guess this means that future AI's should be able to lie in situations it deems profitable