Medicaid and claiming a dependent

I live in a house hold of 3. Myself, my girlfriend and our son. According to her, when she filled out the forms for both of them to receive medicaid (I have my own ins.) It asked if she would be claiming him as a dependent on her taxes (apparently this is the only way she would qualify?) so she said yes. My question is, why does them having medicaid, mean she has to claim him on her taxes? Why can't I?