I'm thinking that Khan (hey I kind of got a thrill typing that..) made the little girl sick in the first place. There wouldn't be much they couldn't cure but I'm sure he came up with something. Identified someone in the right position he thought would be vulnerable, targeted his family and then offered him a solution. What I don't understand is why Khan didn't just blow the place up himself when he had access to it? Is it because he wants to erode Starfleet from the inside by freaking them out that one of their own could do that?
I also don't understand why Marcus thought there was any safety in allowing John Harrison to hang out in Section 31, surely the most dangerous place ever to install a eugenics superman. It seems that initially Khan had him sucked in and he believed they were working together.
When Marcus tells the assembled captains that the transmission he received from the bomber says he was being "forced" to do it by John Harrison it made me think that the bomber wasn't just offered his child's life, he was threatened with losing his wife or other family members as well.