The "compromise" is, bluntly, asinine and economic nonsense. It is a political dressing-up of the same program, meant to confuse opponents through a veil of economic subterfuge. The Wall Street Journal outlined the argument well:
...[Y]ou almost have to admire the absurdity of the new plan President Obama floated yesterday: The government will now write a rule that says the best things in life are "free," including contraception. Thus a political mandate will be compounded by an uneconomic one—in other words, behold the soul of ObamaCare.Fortunately, many opponents of this ruling have not been duped by President Obama's and Secretary of Health and Human Services Kathleen Sebelius's twisted logic. They correctly stand firm against the attempted gross encroachment into the private lives of individuals. GOP Presidential candidate Rick Santorum summed it up best, "It’s not about contraception.... It’s about economic liberty."
Insurance companies won't be making donations. Drug makers will still charge for the pill. Doctors will still bill for reproductive treatment. The reality, as with all mandated benefits, is that these costs will be borne eventually via higher premiums. The balloon may be squeezed differently over time, and insurers may amortize the cost differently over time, but eventually prices will find an equilibrium. Notre Dame will still pay for birth control, even if it is nominally carried by a third-party corporation.