There are many facets to evolution. One is when new genes are created. Another is the timing of genes. The body turns genes on and off at different times. Though there are about 2% genetic differences between humans and Chimps, there are many unstated differences in timing. The changes in timing allow a much faster mechanism of evolution than gene changes. For example, most mammals leg bones are similar. The main difference is the time the genes are active. The Body has the ability to turn on and off the genes. True, most of this is controlled by non-gene parts of DNA, but it is the body that adds and removes the methyl and other groups that turn on and off the genes.
Another example of environmental influences changing the DNA is cancer. Whether bad sunburns or chemical causes, mutations arise in genes. In a sense, the body causes the changes in DNA. When enough accumulate (often about 5-10) the cancer takes off. Both these might be what the creationist was referring to, but neither makes his point.