The Supreme Court ruled against imposing the contraceptive mandate on for profit religious companies in part because there's a less religiously "burdensome" alternative in place for non-profits: the insurer foot the bill and the government reimburses them. The justices suggested that President Obama should just make that accommodation available to the Hobby Lobbys of the world. Unfortunately, that accommodation only works smoothly on paper.
According to Bloomberg's Alex Wayne, under the current system the administrator of a religious non-profit's health plan pays for objectionable forms of birth controls, and the government reimburses them. The third-party administrators say the government doesn't have a way to pay them back yet.
Here's how it should work: the third-party administrator would either find an insurer to cover the cost of the birth control, or pay for it themselves and find a partner insurer through the exchange. Then, the government reimburses the insurer and, if necessary, the insurer reimburses the administrator. But administrators who aren't tied to insurance companies haven't been able to get insurers to agree to that deal and the Department of Health and Human Services says they don't have the legal authority to pay the administrators directly.