The Little Sisters of the Poor and Some Sincere Questions

Unsurprisingly, the New York Times thinks the Little Sisters are being unreasonably stubborn, that they've been "given" everything they want and still "won't take 'yes' for an answer."

After all,  religiously affiliated groups,

"like universities, hospitals and social-service groups, [were] offered ...an easy way to opt out: Notify their insurer or the government, in writing, of their refusal to provide coverage."

Seems simple enough.

"This accommodation struck a reasonable balance between the government’s respect for religious freedom and its strong interest in carrying out the law’s mandate."

This is a little hinky, implying that the "government" was bound by the same law as the Little Sisters, with it's see? there's nothing we can do phrasing - as if it isn't this government itself that created the law and all it's nooks and crannies, as if Obamacare was some outside force.

But no matter.

What I want to know is, this idea that if the insurer is notified, like Pilate, the purchaser of the insurance has washed it hands of the mess.

The insurer provides the contraceptive coverage?
Out of the goodness of its heart?
Or out of the payments made to it by the purchaser, with a wink-wink, nudge-nudge pretense that it is coming from some other source?

Where does the money ultimately come from, and if it's from the Little Sisters, how are they no longer complicit in what they consider an absolute evil?