No, the school does not pay for coverage for anyone. It offers insurance to its students as a plan sponsor. It doesn't want to sponsor a plan that covers birth control. You're claim that the school objects to paying for coverage (like your argument that people want some thing for "free") is baseless.
Ah, so you are upset that their portfolio doesn't include insurance that you want but can obtain from other means?
That too does not curtail your right to obtain the commodity. You argue the absurd. The current argument is whether anybody should be forced to pay for this particular commodity other than the recipient. People actually are arguing that a substance that is easily obtainable is being refused to them because somebody else doesn't give it to them for "free".
My argument is, people can choose to go to a different school, that she was driven to attend this one doesn't change that reality. That contraception is available by myriad means puts false the argument that there is a compelling reason to force any entity to offer a commodity that they find morally and religiously objectionable.
She could obtain this, and did, by an expensive choice. Or she could use the sliding scale offered by Planned Parenthood, or she could purchase insurance from other than the schools offers, or...
Well, there are many choices she could have made rather than attempt to force others to give her something.