Ok, DNA changes occur, but physiological writing to the DNA does not happen in humans. I'll give you DNA repair, BCR/TCR rearrangement, meiosis, and also the more recently discovered LINE-1 retrotransposons - but they occur at specific times and usually in a random fashion. I don't think this fits any idea of what memory is.
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.
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...