Non-coding DNA correlation with rate of evolution
Whether or not species with less non-coding DNA evolve faster, the assumption that this could be explained by their genomes being more susceptible to mutation would seem to me to be based on a false premise.

Let us examine the logic of the assumption by making an analogy to drawing of tickets from an urn in a lottery. If you buy one ticket (coding region), and only one ticket is drawn (there is a single mutation) from the urn (the whole genome), the probability of winning (your gene suffering a mutation) decreases as the number of tickets (the size of the genome) increases.

So the question is “does mutation follow this model?”, i.e. are the number of mutations in a genome independent of its size? To answer this, let us look at two examples of known mechanism of mutation.


Misreading during DNA replication: Here (and in other types of misreading) the error frequency is, quite logically, related to the number of bases replicated i.e. it has a specific (if very low) value of n per 1,000,000 bases — not n per genome.
UV radiation: Here the source of the radiation is external and its flux will be proportional to the area it strikes — hence the larger the target area the more interactions with thymine causing dimerization. Although our linear-centric view of DNA tends to ignore its area, the larger the genome, the larger the target. The only way I can see the non-coding DNA buffering the coding DNA from radiation is if it somehow formed a protective shell around the latter. I know of no evidence that this is so.