No, they don’t. I really invite you to read their paper to see that this is wrong. What they’ve done is to examine the genetic changes arising within H1N1 from 1918 to the present. And what they found is stated in their conclusion below:
While there have been numerous adaptations within the H1N1 genome, most of the genetic changes we document here appear to be non-adaptive, and much of the change appears to be degenerative. We suggest H1N1 has been undergoing natural genetic attenuation, and that significant attenuation may even occur during a single pandemic. This process may play a role in natural pandemic cessation and has apparently contributed to the exponential decline in mortality rates over time, as seen in all major human influenza strains. These findings may be relevant to the development of strategies for managing influenza pandemics and strain evolution.
To sum up:
- they document the numerous genetic changes that occurred in the H1N1 genome throughout its history.
- they provide evidences that most ( but not all) of these genetic changes not only are non adaptive but also likely degenerative.
- they note that the mutation accumulation is associated with the historical exponential decline in H1N1 human mortalities
- by combining 2) with 3), they (rightly IMO) suggest that the decrease in the bug virulence, far from being adaptive, is due to genetic entropy.