Mentally ill or "crazy" people may still be able to think logically. Having experienced psychotic episodes that included planning "bad" things, I can assure you it did not interfere with logical planning. Recounting it later, the clarity of thought was quite clear, disturbingly. The Unabomber is a well-known example.

Someone's goals, utility functions, and even certainty values for some beliefs may be very different than "normal", but it doesn't mean they aren't able to reason logically within those constraints.