Specifically, why do so many of them acquiesce about the use of the term Mormon? As someone else pointed out, the church simultaneously claims that they are not Mormons and yet doesn't want anyone else to use that name either. And for the most part, the media goes along with this, especially in the United States. The thing is, without an explanation as to the fundies' Mormoness, there is no way to gain the true context of the Warren Jeffs thing or other, similar cases.
You see similar stuff with the church's insistence on using Church of Jesus Christ of blah, blah in all the articles even though it's clunky and means less to the average reader than saying the Mormon Church.
Well, to me it speaks to the lapdog-ism of the contemporary media. The church is rolling in dough, while it's not a large market force compared to some, it does have some key people in high places and it is a fairly organized "interest group" that is aggressive about its interests and the lapdogs won't bite it.
On the other hand it could just be the laziness of the contemporary media. They could do a very respectful, respectable job of clearing up the issues--let the church spew about who's mormon and who isn't (well, nobody technically--don't call us mormon, but don't call THEM mormon either because they have nothing to do with us). Instead they do a press-release kind of journalism and just reprint statements from the institution in question. Much easier to meet the deadline that way. None of that pesky digging, parsing, and nuancing involved.