I do not understand their thinking at all.
The reason many right-leaning groups (esp. the NRA) dislike relaxing of the FCC regulations is that they're afraid that if smaller market TV/radio stations are bought up by large media corporations run by liberals (such as Tribune, NY Times, WashPost, Viacom, etc.) they will have a harder time running politically incorrect advertisements and such.
To a degree, this fear is correct since in a certain sense, large media corporations do not operate have to respond to the free market because of their size. A good example of this is the broadcast television networks. If ABC, CBS, or NBC decided to present news in a consistently unbiased manner, it would undoubtedly bring them success as FNC has shown. But this doesn't happen because, as former GE CEO Jack Welch argued, the network news divisions are extremely puny portions of the overall revenue pies of Disney, Viacom, and GE.
So any executive who'd like to make his network news more fair generally avoids doing so because to attempt to do so would generate a lot of negative publicity for very little potential economic gain.
Nor is it just the case with the news divisions only. It's also the same reason why you never see sitcoms or dramas with conservative themes while many shows have liberal themes in them.
The issue is a difficult one to sort out and far more complex than the WSJ makes it out to be and there are both positive and negative aspects of the Senate's actions.
_mws_