yeah.. you can either use a tv tuner card and connect your cable to your computer and get the screen picture captured or even record the video. However if u are asking to take a photo snap of tv screen, reduce brightness of camera and tv to match intensity of both. Then u get a clear picture.
I am agree with you. If the shutter speed of your camera is too low, you may end up capturing a highly blurred image. Its important to adjust your shutter speed in accordance with refresh rate of your TV.