Of course there's a lot of other stuff RNA can do like catalytic activity, triggering RNA interference or reacting to other molecules (riboswitches). But information storage isn't really anything RNA is known for.
Although I'd again argue that there is no single "true" medium or mechanism of memory.
I'd remind you that DNA is indeed memory. It's memory whose recall is heavily modified and contextualized by its environment, for example methylation, the topology of how it is currently twisted, the kinds of nutrients available for molecular synthesis, etc.
If RNA mediates memory on a sub-generational timescale, it seems that it'd provide a dynamic, contextual bridge between generational memory in DNA and shorter term kinds of memories that play out over timescales less than an individual's life. So that the molecular formation of a given memory would have a semantic basis in the longer term context. A concrete but way oversimplified example of this might work:
You go through a traumatic experience where you almost die. The specific way you almost die is related to a number of factors involving your ability to run fast enough. The long term memories of that experience are then encoded as proteins by a mosaic of genes related to certain muscles, their shape and size, certain metabolic pathways, etc. The way we might unpack or interpret that memory at any given time/context could be as a gutteral impulse that results in such realizations as "I need to get more exercise" or "my grandparents had heart disease, maybe I should go to the doctor" or "wow I'm sure hungry for fish", etc.
Btw I'm not even arguing that it's as clear cut or simple as that, just sharing how I intuitively make sense of all this evidence and these hypotheses.
So as an simplified analogy, the DNA would be like a dictionary of common words that could be used to encode a meaningful story about something the organism has experienced. The RNA would be like the handwritten copy of each word as the story is written down on a piece of paper. The paper with the handwritten story is analogous to the proteins that have been shown numerous times to be involved in long term memory storage and recall.
Yes, it contains information. But you can't write to it.
My hunch is that you're thinking of memory as being equivalent to RAM in a computer. So I'll remind you that read only memory is still memory.
Some microorganisms, like viruses, do directly modify DNA. That's where CRISPR came from.
I'd encourage you to check out the full range of definitions of the word "memory".
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.
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.
Viruses integrate into the human genome, then decay and eventually become fodder for new regulatory regions and genes.
During human life, your genome is mutated, and your body repairs it, sometimes making mistakes, which are permanent (and passed down to your children if it happens to the germ line).
I could go on...
If you're saying it's theoretically possible, I would agree that it might be, and that there is a potential for DNA to be memory. But to claim that DNA is memory without a known write process is premature I think.
Well there's lots of information there which can be used to infer aspects of previous states. I assume it's more of this aspect that is being referenced, rather than what is encoded in the RNA.
I am personally interested by the 'RNA Computer' hypothesis which posits an additional layer of differentiation in computations performed by interacting RNA.
I have also read of experiments where memories (learned behaviors) were transplanted by injecting ground-up neural material. Flatworms were the subject I think.
Of course this is all near the edge of mainstream, but I think genuine science demands openness to new ideas.