The reason this might be a plot hole is because of the human element. Regardless of what the Code is (Black Box), we will say that humans have not fundamentally changed. If they have, there are problems with that view too, so let's take a look. One precept, by the way, is the belief that translation is fast very fast, not like reading complex text (since Tank responds in realtime during Neo's escape).
This is the view that humanity biologically and mentally are the same as us. This is the most useful view for explanation or prediction, the x-factor then becomes the Code and how it is interpreted. There can be two views:
1. Literal image. Under this theory, they look at the code and they see a literal image of what is happening. An absolute interpretation of events. This is analogous to to musical prodigy who can read sheet music and "hear" the score. The two problems with this: perspective (where is the "camera" and how is it controlled? Consider that the Operator and those on guard seem to allow the Code to display itself passively) and info overload (this is a common problem with theories, discussed in a bit).
2. Symbolic. This theory is more like reading. One interprets the symbols read into concepts which are imprecise imaginations. The most analogous thing would be an air traffic controller job. They view tons of numbers and generate a picture in their mind's eye. Unlike a literal image, they can not use that picture to recreate the Code in every detail since it is a fuzzy concept not absolute image.
Concrete example: In Literal image theory, it is like getting a photo with a red hat. From that picture you can put into exact terms what the color was. In Symbolic theory, you get text saying "red hat" and it is up to you to imagine what shade of red, but everyone imagines slightly differently.
The problems with Symbolic theory (besides being imprecise): Translation (the image translator for the Construct shows that there is a discrete answer to the code, not simply a concept) and information overload which is one shared by Literal theory. We can solve this in part by making Code reading, part art, part science, something like how we can pick out a face from impressionist paintings. We discard, define, and interpret information in a way that only our minds can. So that only some of the information is relevant. However, even in this case there's simply too much information... there's no analogous human feat today of this scale.
What if humans have been somehow altered to bridge the gap? It cannot be simply the plugs since Tank was born normally. So it would probably be something along the lines of intentional mutation. This borders on creating another Agent Neo type problem with genetic access to the workings of our mind. This might be solved in relation to the machine's motives, seeing the Matrix as necessary but keeping permanent alterations to a minimum.