To display 60hz stereo images, you need a 120hz image and synchronized shutter glasses. Each frame is shown twice, once to the left eye and once to the right. These are interleaved in time and synchronized with the shutters on the glasses that alternately close the left and right eye. To display stereo images, you not only need a 120hz display device, you also need a way to synchronize the glasses with the image. There are some methods that patch into the video stream and use the vsync there, there are some that plug into the television itself and are triggered by actual frame changes. Note that progressive scan LCDs tend to be terrible for stereo, because not all of the image updates at once, and thus each eye sees some of the image meant for the other eye (and you get blurring and the stereo illusion breaks).
I watched a 3d movie on a lcd screen that's not 120 hz (it's less but i'm not sure what hz it was). I saw the 3d image, but it was horrible. It was not pleasing to watch at all. I'm guessing this was due to the "each eye sees some of the image meant for the other eye" idea you pointed out. So this is what 3d tv's are meant to do...improve 3d viewing capabilities, not necessarily create it?
Watching 30fps stereo on a DLP projector running at 60hz is a pleasure. It's not so much the framerate as the fact that an LCD screen does not update the entire image at once, but scans through it one line at a time. This way you don't have a single time point where the entire image is just left or just right. Updating the entire screen at once, at 120fps, is what 3d televisions (and DLP projectors) do, in addition to providing an external sync trigger signal for shutter glasses to latch onto. That is what makes a display device 3d compatible, not the frame rate in itself.
That said, if you have a high enough framerate on an LCD you can simulate the global screen change effect by just showing each frame longer, for example running a 120hz screen at 30fps stereo (60 fps total), and showing each frame twice, giving the screen time to update.
