Three things...
1. This is Politico, who will twist and turn any story to make Republicans look bad. Especially to Republican voters.
2. Do you really think the GOP House can keep the rule from taking effect? Doing so would require the approval of the Senate (not gonna happen) and the approval of the White House (not gonna happen, either).
3. The GOP House, the GOP Senate minority leader and the GOP Presidential candidate have all promised -- straightforwardly -- to kill Obamacare if they win the Presidency and Congressional majorities in the November election. Kill Obamacare and the contraception issue is closed.
Thus, the House didn't cave, as you suggest. Instead, they chose to save their bullets for a battle they could win. The same thing you would do if you were in their position...
I get frustrated with some people here some times, they are easily manipulated by the likes of Politico.
Sen Jim DeMint has already outlined the strategy. I just posted it.
That was my thought, as well. The MSM will do anything to try to damp down the Republican vote this year. It is the ONLY way that Obama can win.