Umm... You can't continue to use your apparent definition of "information" and argue with the math/science guys at the same time. There is a very precise mathematical definition of information that is used in science and math (and economics and engineering, etc). For starters, an increase in entropy causes an increase in information content. Anything that increases the entropy of DNA is increasing its information content, and for better or worse (depending on the situation), most things that modify the DNA (viruses, random chemicals, radiation) generally either increase the information content or destroy the DNA. So random natural processes are creating "new DNA information" all the time. In fact there are processes in the cells that have the function of preventing the addition of new DNA information to protect against the fact that it happens frequently.