Basically, the Weigel lab looked at the mehtylome of Arabidopsis thaliana (mustard weed, the Drosophila of plants) across 30 generations in 10 separate lines. They found that methylation of individual cytosines changed three times more quickly than the rate of DNA mutation. By contrast, wholly methylated regions (for example, at transposable elements), mutated at the same rate as DNA mutation. Additionally, the different lines showed similar methylation patterns.
So what does this mean for evolution? Well, we have to think about methylation that affects functional genes versus methylation that supports architectural integrity. Methylation at transposable elements probably keeps them from jumping, whereas methylation at an individual cytosine might be affecting the functionality of an exonic region. We are still in the infancy of understanding exactly how epigenetic mechanisms impact evolution, but I find the claim that "epigenetics are not important for evolution" to be sadly misinformed. Even when epigenetic marks are not as heritable as DNA marks, they have very important implications for the (non)heritability of traits! And that, my friends, has everything to do with evolution.