The problem with this logic is that the alternative to free contraceptives isn't no contraceptives. It's that the woman pay for those contraceptives herself. And that's exactly what that woman did at Georgetown. She spent her own money, and bought contraceptives. So her argument doesn't come down to an inability to pay for contraceptives, but rather, her selfish desire to spend the money she's spending on contraceptives on something else.
Why in the world should the rest of us support her spending habits?