Can my 120Hz tv really only handle 60Hz HDMI input?

The 120 Hz factor is all generated by your TV: it is generating "in-between" frames that are a mixture of one frame and the next frame (1/60 second later) as an in-between frame to attempt to smooth out the motion. The source is still 60 Hz, but the number of frames is doubled by the TV's video processor. Confusing, maybe, especially when you factor in the fact that 3D television requires a true 120 Hz source. So no, it isn't possible to convert a 120 Hz standard HDTV into a 3D TV.