Can my girlfriend claim my children as dependants?

I am a full time university student and my girlfriend pays all of our bills. We have lived together everyday this year. A tax preparer told us she can not claim my two children for earned income credit because we are not married and she is not biologically related to them. Is this accurate? My childrens father did not work this year and neither did I so we are not eligible to claim them. I thought they would qualify because though we are not married she is their "step-mother."