What's ridiculous is that FMLA can't be used against sick time. Wife have a baby and need time to be with them? That's gonna cost you (unless you have unused vacation or you're in the right state).
I experienced a significant tragedy a couple weeks ago, yet I couldn't call in sick for it (legally)... only FMLA... despite being clearly unfit to come into work.
It needs to be clear that the company in those situations behaves like a saint... absolutely incredible how they go out of their way to help. Just with the contract and the way FMLA works, sorry... you're out the money.