A short summary of the some technical aspects of Artificial Intelligence would help to make clear the central issue of this article. If we are considering the sorts of active AI entities typical to science fiction works, whether bodied or electronic, then these agents are likely to have classical AI structures, at least when viewed from an external viewpoint (if not also internally as part of the agent's implementation). These structures include: a perceptual mechanisms, a world knowledge database, a short-term working memory subsystem, common-sense knowledge, a planning ability, an actuator mechanism (e.g. a speech or robotic motion subsystem) and a reasoning mechanism.
Central to this article is the reasoning mechanism. If we augmented a human with an infrared vision system or a mechanical prosthesis, then we wouldn't think of the human as being more than physically enhanced. Similarly, if we added access to a larger knowledge base or greater memory, we would be impressed with the human's abilities, but would still consider him/her to be enhanced but essentially human. Thus, if anything, it is the reasoning mechanism that sets the AI agent apart from humans.
The classical understanding of AI reasoning mechanisms is that they are all variants of logical reasoning. These include a variety of pattern matching and manipulation systems (e.g. production systems) or explicit logic (e.g. of the familiar form ``All men are mortal'' plus ``Socrates is a man'' therefore ``Socrates is mortal''). Mathematically, all known sophisticated reasoning mechanisms are equivalent (i.e. there is nothing that you can conclude using one method that can't be concluded when using another method, although you might be able to do it faster using some methods). The mechanisms have also been proven mathematically to be fundamentally limited (i.e. Gödel showed that there are things that can be seen to be true by humans in even simple formal reasoning systems but these things cannot ever be proved). Current computers are based on these logical mechanisms, so some people argue that they can never be intelligent. At least they can never act like humans, since humans never act so perfectly logically.
Much has been made of the recent success of the computer program Deep Blue's challenge to the human world chess champions. But, Deep Blue's skill comes from a very different mechanism than human skills: it is extraordinarily fast, has special computer components specifically for chess playing, has access to thousands of stored previous game situations and has perfect memory of its reasoning. Humans cannot match this, but have better judgement about what is or is not a likely strategy, and have good heuristics (``rules of thumb'') about what to do and when. Deep Blue can only play chess.
Chess and mathematics are domains where ``exact'' reasoning skills are taken to the limits, but these are exactly where computers have strengths. When it comes to other activities, such as teaching a person a new skill, human reasoning approaches (so far) are much more successful. When playing chess, we can recognize the essential details of a situation and its similarity to previous known situations, know various strategies that might be applicable, and have judgement about what might work. We also make lots of mistakes, which can lead to new discoveries that a more formally correct machine might not make.
So, to give an exaggerated summary of the point: human and AI reasoning mechanisms are currently and are likely to remain quite different. Thus, the consequences of that reasoning will be different - the choice of evidence used, decisions made and actions taken might be quite different for an AI agent, and thus unintelligible to humans.