Media criticism has been an ongoing focus of mine for many years and those Shorenstein Center studies, which have been around for years, fall into the same trap as many other dilettantes in that particular field. “Tone” is something to compliment serious media criticism; it’s rarely any sort of solid foundation for those who try to use it as a focus and that’s for the very reason you outline from multiple angles: it’s resting the whole shebang on subjective judgments.
I was writing about this re:Shorenstein back during the 2008 cycle, when the Center was repeatedly using this same methodology to claim Obama was getting far more positive coverage than negative. The stuff being coded as positive was any reporting that Obama was leading in the polls, had just raised a lot of money, was drawing crowds, etc. The press was being tarred with a pro-Obama bias merely for reporting basic facts of the campaign. This approach suggests a nonsensical notion of “neutrality” is the preferred option. When campaigns suffer setbacks, candidates make gaffes, scandals erupt, etc., reporting on these matters ends up coded as negative. Are journalists supposed to simply not cover those things? Perhaps come up with some quota of positive stories to make up for the ones covering the bad ones? It’s all just sort of silly. And so are the Shorenstein Center’s tone studies.
That’s not to say the Center’s work is entirely worthless. Among other things, it documented the severe lack of issues coverage in the last election cycle. That reflects the campaigns themselves, particularly the Clinton campaign, which spent almost all of its time trashing Trump and avoiding issues — that’s why Clinton’s current complaints about this aspect of the coverage are bullshit — but it’s the job of the press to dig into policy matters and inform the public on where candidates stand and it has been failing miserably at this for years.