Obviously a tad miffed about being portrayed as a radical Muslim instead of the mdoerate Christian that he is, Barack Obama has reportedly been freezing out FOX News in the last few days. Roger Ailes has reached out to Obama and since FOX News Channel is by far the biggest news channel, this probably won't last. But it's nice to know Obama can push back against lazy smear campaigns with some effect. This is a perfectly reasonable move and perhaps Obama has rightly decided that no one at FOX will give him a fair shake.
But in general, I'd counsel freezing out the specific writers and editors behind a story rather than the publication or news outlet as a whole. "Fox and Friends" and specifically host Steve Doocy is the one who deserves to be frozen out, along with anyone who repeated it on FOX and didn't rush to run a correction when the truth came out. (The truth is that the source of this scurillious rumor was a far right website, Insight, that depends on anonymous sources for stories written by anonymous reporters. It's the political equivalent of the National Enquirer, or more accurately Weekly World News.) Similarly, if a top reporter at the New York Times does you wrong, freeze them out, not the entire publication which has hundreds if not thousands of reporters and freelance writers, all with their own standards of excellence or lack thereof. I've been frozen out myself by celebrities because of something written by someone else I'd never met in another department at a newspaper who may not even be working there anymore. Hold people responsible for what they write and report, not what others write and report, even if it's on the same media outlet and you find that outlet -- FOX -- generally shaky in its journalism.