From the abstract:
"According to classical thought, DNA damaging events and mutations occur randomly throughout the genome of organisms purely by accident. However, a growing body of evidence demonstrates that some genetic change occurs in non-replication, non-random events."
That raises two flags right away. From the very start, the randomness of mutations has always referred to fitness, not to the region of the genome. In fact, we discovered that mutations were random before we discovered DNA. When we say that mutations are random we mean that the processes that produce mutations are blind to the needs of the organism.
The second red flag is the use of non-random events. This is a bit like saying that the lottery is non-random because it takes place on non-random days.