Mike,
I would still go with Unheralded Victory by Mark Woodruff. The premise of his book is to first illustrate how we won the battles beating both the Vietcong and North Vietnamese troops. The last 1/3 he talks about all those things the media reported, the "myths" that were created, and how they influenced public opinion. His theme is we won the battles, but the media lost it for us, and here are the untruths they told to lose it for us.

"How Democracies Lose Small Wars" covers the subject to some degree as well. Gil Merom talks about societal factors which influenced the press, which in turn influenced society to degrade support for the war.

Those two would probably be the best of the 3 I previously recommended.

Also, If you haven't read through the 1947 commission report "A Free and Responsible Press" it can give you some background on why the press reports subjectively rather than objectively, beyond everything being filtered through the prism of one's own perspective.