There is nothing special about DNA replication. It’s just a nearly deterministic physical process that produces a chemical that’s happens to be easy to think of in terms of digital information. But the production of mutual information is a ubiquitous feature of natural, deterministic processes. There are correlations all over the place in the real world – between the temperature in my block and the temperature on the next block, between the density of crabgrass in front yards and density of crabgrass in backyards, between the time of year and the amount of sunlight, and on and on. Such correlations exist because causality is a feature of reality, and the closer a system is to being perfectly deterministic, the stronger the correlations and the larger the mutual information between different products of the same physical cause. Mutual information exists, and has to exist, because of determinism, not in spite of it. Mutual information between two cancer genomes, or any two offspring genomes, is created because DNA replication repeatedly produces the same product (more or less) over and over again. That is the physical reality that is being modeled in terms of mutual information. Any argument that concludes that determinism cannot produce mutual information is incoherent.
It seems to me that the central issue is what the information no-growth theorem actually says and what it applies to. That might be a more fruitful area to explore than whose implementation is correct.