You probably erred when you used the term "specious" above. As for DNA appearing digital, I'd agree somewhat.
However, DNA more closely resembles an analog computer (or control system) than a digital computer, to me.
And specific changes in an analog control system are not always 100% predictable due to environmental feedback. Hmmm...
Interesting that analog us reproduces with DNA, which is clearly digital in structure. Some mechanism must be required to prevent the iterative ADA conversion from drifting into nonviable jelly. Is it possible that the mechanism is selection?
What quantity of information is encoded in DNA? Unless you can explain it, then information theory would indeed seem a poor choice for chemistry.