I think you are right. Either they have accidentally used the Earth's field somehow, or they are mistaking other effects (drag, perturbations...) for a thrust.
I would tend to think it uses Earth's magnetic field. Magnetizing or demagnetizing a moving mass would make its potential energy vary inside Earth's magnetic field. This may occur without reaction (I am not sure about this, my physics courses are far away and magnetic material physics is not that easy). Once they varied the potential energy of the moving mass, they would actually move it inside Earth's magnetic field, leading to a reaction force. The reaction force would be greater in one direction because of the cyclic magnetization/demagnetization.
And if the satellite's orbit is not perfectly circular, you may even be able to gain altitude by moving a mass at specifics times, like a kid on a swing or a skater in a ramp.
