If we're technical, there is a substantial legal difference between your brain and an AI system, because the criteria for what counts as a copy is defined (in US) as "“Copies” are material objects, other than phonorecords, in which a work is fixed by any method now known or later developed, and from which the work can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device. The term “copies” includes the material object, other than a phonorecord, in which the work is first fixed." and all the law precedent doesn't consider any representation of something in your brain as "the work being fixed" , so that isn't a copy and anything that applies to copies doesn't apply to your memory, but do apply to any computer memory or any future technical method to make that representation.
So analogies to the brain aren't appropriate, because human memories are special and separate in the eyes of law, and if we'd make a machine that does literally exactly the same thing as your brain does, it will still NOT have the same legal treatment as your brain; there is no legal principle that it should get equal or similar treatment.
I don't see why brains don't satisfy the legal definition, if I have truly memorized the book, unless you are trying to claim that brains aren't material objects. Encoding a book by tattooing it on my back would count, wouldn't it? Or by encoding it in DNA and injecting it into some of my cells. Why would using the brain be different?
The definition of a "copy" requires it to be fixed in a tangible, durable medium. This law has explicitly chosen to make a strong, major black&white distinction between intangible things and things that are fixed e.g. on paper. According to legal precedent, memories in human brains are considered these intangible things and not considered fixed in a tangible medium, ergo, those do not count as "copies" as far as copyright law is concerned.
Tatooing on your back or a fixed encoding would IMHO indeed probably count as fixed in a tangible medium, but that's not really relevant. And there is some argumentation about why using the brain is different (e.g. that it does't permit the unchanged reproduction of the information stored, memories tend to be fleeting and incomplete), but again, that's not relevant and any flaws in that argument don't really matter.
The key point is that the argument is settled. It doesn't matter what argument you or I could make about whether using the brain is different or the same, no one cares about that argument, we have no right to re-try that question, because this discussion has been heard by the relevant courts, and it is over - it's now part of settled law, and it doesn't matter if you now figure out a better argument or the original argumentation was shoddy, the discussion is finished, and your opponent effectively has the right to demand that the judge ignores your argument and instead apply the existing case law.
As it has been legally "accepted" in precedent that memories do not count as fixed on a tangible medium, then that sticks, that effectively becomes part the legal definition of what "fixed on a tangible medium" axiomatically means. Any appeal to biology/physics/whatever is pretty much irrelevant - if future science comes up with incontrovertible evidence that indeed memories store a fixed, durable, unchanged copy and are literal equivalent of tatooing a copy on your back, that doesn't matter, all it means that the colloquial understanding of "fixed on a durable medium" (which then would include memories) has diverged from the legal definition of "fixed on a durable medium", which does not.
If you want to apply logic, in this context "memories don't count as fixed on a durable medium" is an axiom - changing it is possible by passing new law, but not purely by some arguments that it should be treated differently; a key common law principle is that we assume that the earlier cases have been correctly decided and don't re-litigate that with new arguments.
So analogies to the brain aren't appropriate, because human memories are special and separate in the eyes of law, and if we'd make a machine that does literally exactly the same thing as your brain does, it will still NOT have the same legal treatment as your brain; there is no legal principle that it should get equal or similar treatment.