An imprint of history is not memory, in much the same way that fossils, stars, the environment is not memory. Human DNA has not been written to. It is edited in only very specific circumstances - DNA repair, TCR/BCR recombination, meiosis and interestingly, and possibly relevant - LINE-1 transposons in neural tissue.
Why not? They encode state in a way that is stable over time. Any medium that preserves state over time can and likely does function as memory in some way or another.
At any rate, DNA encodes useful information related to how an organism's ancestors were able to survive their environment. If you prefer not to call it "memory" for semantic reasons, I don't really care too much, although my opinion is that memory is too deep of a concept to be narrowly confined like that. Nevertheless, even if you don't call DNA memory, it doesn't change my point in the comments above, which is that the information encoded in DNA is directly relevant to any survival related memories, and so it would make a lot of sense if such memories were formed in direct, physical reference to that information. Seeing as how it's been shown that protein formation is involved in memory formation and recall, and seeing as RNA is how proteins get their molecular structure, it's not a far reach to see the possibility that RNA is a contextual bridge for memory to be encoded in reference to survival related information provided by DNA.
None of this requires that DNA be writable in the same way that transistor based me let is writeable. DNA is written through a probabilistic, distributed process, but it still encodes information about the molecular tools its carriers successfully managed to survive and reproduce with.
An imprint of history is not memory, in much the same way that fossils, stars, the environment is not memory. Human DNA has not been written to. It is edited in only very specific circumstances - DNA repair, TCR/BCR recombination, meiosis and interestingly, and possibly relevant - LINE-1 transposons in neural tissue.