Good points. This study, like any good academic study, is limited and focused. All it sets out to do is examine the rate at which media outlets cite various think tanks in pure news stories and rate political orientation of the outlets based on the think tanks used. The political orientation of a think tank is determined from how often it is cited by Congressman and Senators with known political biases.
The result is limited in scope and far from proving a liberal media bias. The conclusion is simply that most media sources cite the same think tanks as a moderately left of center Congressman in news stories. Implicit is the assumption that elected Democrats and Republicans are accurate barometers of liberalism and conservatism as a whole, which is perhaps the weakest link in the study. There also does not seem to be any discrimination in what types of stories are reported because that may well affect the think tanks consulted. And, like you pointed out, editorial content, in particular editorial comments by anchors during a broadcast, is an important factor in media bias.
In sum, the result is something most people accept: the news is reported from a moderately liberal perspective. Claims that conservatives dominate the news or that the mainstream media is far-left are not supported by this study. Given that reporters describe themselves as socially liberal but economically conservative, this is not that surprising.
Now, it'd be instructive to see a similar study on editorial content in news broadcasts with the same level of objective rigour or a study looking at which Congressman and Senators are cited in reports since that is even more direct than the methods used in this study.