In addition, the very fact that Francis Crick decided to study consciousness in the first place may – or does – suggest that he couldn't have been a reductionist in any strict (or traditional) sense. After all, in much psychology, neuroscience/neurobiology and sometimes even in philosophy consciousness had been reduced to brain/behavior or simply ignored. Then again, most of The Astonishing Hypothesis is about neurobiology. Thus, even though the opening quotation is in essence a philosophical position, the philosophical defence and implications of that passage are rarely fully developed in the book itself.
It is true that the memory (as a mental event/state) itself is about a cat's death in a river. Is neuron set x also about a cat drowning in a river? The memory itself relates to something which occurred in 2010. Does neuron set x also relate to an event in 2010 - at least in the same way as the (mental) memory does? Inversely, brain part x is grey-pink, fleshy and three-dimensional. Is the memory of a dying cat also grey-pink, fleshy and three-dimensional? And so on.
To repeat: although the memory is indeed dependent on a part of the brain, it can't be identical to it. To paraphrase Leibniz again:
More accurately, take the case of a particular ambition of a particular person at a particular point in time.
Could that really be fully accounted for by the brain alone (or by a set of neurons)? If it were, then perhaps a neuroscientist could look at that set of neurons and literally either see the ambition or get to knows its content in some other way.