For instance, ionizing radiation doesn't have a preference for particular bonds in DNA, but because DNA, in situ, is tightly wrapped in chromosomes with associated proteins, the actual effect of free radicals is only on exposed parts of the molecule. It's random, in that it is non-specific or undirected, but the effect of mutations in the DNA are not random.
Your's is a great example of external conditions provoking what would be called a random mutation.
Another might be the example of the two genes in that antarctic fish (April 15, 1997 - Proc. Natl. Acad. Sci.) where one codes for trypsinogen and the other codes antifreeze glycoprotein. It was inferred that the divergence would date back some 10 million years to comport with environmental pressures. Critics argue both genes (or the ability to mutate) were already there, that there was not enough time to go through the necessary steps without extinction.
I assert that whereas random mutations no doubt do occur, that the ability to mutate is encoded in the genes - that mutations are more often opportunistic than random as the organism tries to fight off invading viruses, protect itself from the environment or take advantage of environmental opportunity. I came to this conclusion based upon these sources:
The Physics of Symbols: Bridging the Epistemic Cut
Complexity International Brief Comments on Junk DNA (pdf)
Language Like Features in Junk DNA
Natural selection applies in either scenario, so why would anyone want to 'throw the baby out with the bathwater?'