The debate over the Hobby Lobby case has been plagued by many problematic presumptions, but there's one that even many people who disliked the decision seem to sign on to without thinking about it. It's the idea that the health insurance you get through your employer is something that they do for you—not just administratively, but in a complete sense. But this is utterly wrong. You work, and in exchange for that labor you are given a compensation package that includes salary and certain benefits like a retirement account and health coverage. Like the other forms of compensation, the details of that insurance are subject to negotiation between you and your employer, and the government's involvement is to set some minimums—just as it mandates a minimum wage, it mandates certain components health insurance must include.
Those who support Hobby Lobby are now talking as though mandating that insurance include preventive care is tantamount to them forcing you to make a contribution to your local food bank when you'd rather give to the pet shelter. You can see it, for instance, in this piece by Megan McArdle in which she tries to look at the clash of rights involved in this dispute, but running through the whole piece is the idea that an employee's health insurance isn't compensation for her labor but a piece of charity her boss has bestowed upon her for no reason other than the goodness of his heart. Referring to the question of whether the religious beliefs of Hobby Lobby's owners are being imposed on its employees, she writes: "How is not buying you something equivalent to 'imposing' on you?" Then later she refers to "a positive right to have birth control purchased for me."
But when your insurance coverage includes birth control, your employer isn't "buying you" anything. Your employer is basically acting as an administrative middleman between you and the insurance company. Your employer isn't the one whose money is paying the premiums, you are. It's compensation for the work you've done, just as much as your salary is.
This goes all the way back to to the roots of our employer-based insurance system. During World War II, the government imposed wage and price controls, meaning employers couldn't give raises. So they began to offer health insurance as an alternate form of compensation, and when the IRS decided in 1943 that insurance could be paid with pre-tax dollars, it made it all the more attractive as a form of compensation. And keep in mind that the preferential tax treatment of health insurance (which the self-employed don't get) is a tax benefit to the employee, not the employer. If you eliminated it, employers' balance sheets would stay the same (it would still be counted as an expense), but employees would have to pay taxes on the benefit.
You might or might not think that remembering the true nature of the insurance benefit should change the calculation in the Hobby Lobby case. I'm guessing that for the plaintiffs, it wouldn't; they'd probably argue that even having to think about what sinful harlots their employees are imposes a "substantial burden" on their religious freedom. And as I've argued before, we should get rid of the employer-based insurance system entirely. That may happen eventually, but in the meantime, it's good to remember just whose health insurance it is. It's not your boss'. It's yours.