In Hobby Lobby, Alito suggested that his ruling was narrow because the administration could provide the same exemption that it gave to religious non-profits - that if the religious entity objects to providing coverage itself, the third-party insurer itself must offer contraceptive coverage as a rider directly to the employee at no cost.
Well today, not even a full workweek later, the conservative majority has exposed that as a lie. In Wheaton College v. Burwell the Court held over the dissent of Sotomayor that Wheaton College is not required to fill out the exemption form. Wheaton takes the position that it has a religious objection to filling out the form, because by filling out the form the insurer will provide the coverage itself, and that makes it complicit in "evil." The Supreme Court granted an emergency motion for a stay in favor of Wheaton, holding that it need not fill out the exemption form.
In layman' terms, a majority of the Court has decided, effectively, that a religious college can not only opt-out of providing contraceptive services to employees itself, but it can also prevent third parties from doing so despite the PPACA's mandate that all women receive such coverage.
The majority claims that in this case, HHS can instruct the insurer to provide female Wheaton College employees with contraceptive services in this case without the form, but as Sotomayor notes, the only reason HHS even knows the identity of the insurer is because this lawsuit was filed. The logic of this case is that the next insurer can just state that it will not provide contraceptive coverage and then stand mute, not giving the government any information with which to apply the PPACA's provisions.
The Sotomayor dissent is a must read. I am on mobile and can't go more I to depth now, but she says it all.
EDIT: ABC news report on the ruling.