Deductions & credits

I appreciate your attempt to answer my question but you are misunderstanding what I am asking. I already know that a grandparent is not subject to the nanny tax and can report their income as miscellaneous income. My question is does this earned income allow them to make a roth contribution and be eligible for the earned income credit.  Turbo tax processes it in such a way to make them eligible for both the earned income credit and to use that earned income to contribute to a roth account. Is this correct?