To be fair to anyone so motivated: the word "public" wasn't necessary to the comment. Loud, substantial private funding for such an endeavor would presumably solve the problem just as well.
(They also might be thinking that "regulations around reporting" pose a substantial free speech issue.)
I think you presume too much of private entities, which would always put their financial interest first (lead gasoline science studies come to mind, tobacco/cancer obfuscation... etc)... you can't trust a private company not to act in its own financial interests, that's not how they work.
At least with a public entity, you should be able to publicly audit what's happening, and with public funding to answer to, the public's interests and the proposed entity's financial security are aligned properly.
One would counter that if private money was at all interested in resolving this problem they may have done so at any time in the last 3 decades, which is only the most severe the crisis has been, not it's full duration.
One would also counter that regulations regarding the accuracy of speech existed in 1987 and were by most accounts, pretty effective at keeping news informative and balanced, as opposed to after those regulations were retired and we got politics being covered like sports and the political divide becoming larger and larger as time goes on because making people angry and scared of the Other is pretty profitable, while getting them balanced, informed coverage is both more expensive and not as appealing to the consumer.
(They also might be thinking that "regulations around reporting" pose a substantial free speech issue.)