I downloaded the published study and read it. They made two obvious statistical errors, one in interpretation of their results, and one in methodology. This is the type of study that should probably be completely ignored. Unfortunately the internet picked it up and now people are talking about it.
In interpretation, they made the common mistake of concluding that there is no difference on the basis of not finding a statistically significant difference. This is just the wrong way to interpret the results. This error is logically equivalent to not collecting any data at all, being unable to detect a difference, and then concluding that there is no difference. This is a stats 101 error.
In methodology, the paper claims they did a one-way ANOVA, which means that they did not account for differences among runners. If you look at the pictures of the data they provided, there is a large amount of variation among runners in the variables they collected, but they didn't account for this in their statistical analysis.
Some further thoughts:
They measured 6 acceleration variables, and the average on the paved surface was higher than on dirt in all 6 of them. They were higher on paved than on gravel in 5 of the 6, and equal on the other one. Some of the values are 5-10% higher on paved. This seems to me like an amount that could potentially make a difference in injury rates.
The accelerations varied by a factor of 2 among the different people. I'm guessing this has to do with weight.