Technically, it's Jack's job to deal with personnel issues; he is the boss. But Suzie is a twenty-first century woman, and his second-in-command to boot. When Jack is part of the problem, it's her duty to handle it.
Of course, she doesn't intend to make friends, confront her own dubious morality, or admit to having a heart; but that's okay. She's Torchwood. She's flexible.