I wonder if there may be a grain of truth behind this.
Assuming that the laptop is being asked to decode and output several hours of continuous video streaming (HD?), the card will be driven quite hard - certainly I see an increase in temperature on my desktop graphics card (and the fan speed increases) when doing graphics intensive work, such as watching HD videos.
I don't have a problem with my desktop overheating, but it's possible that a laptop could be much poorer at dissipating the heat, causing the GPU to overheat.
Having said that, it would be the same using the laptop's own screen or using any cable to an external screen - DVI, VGA or HDMI. I'm assuming that the resolution is the same - the laptop's own screen resolution is likely to be higher than any TV screen.
What you could do is to download SWI (or similar) and monitor the GPU temperature while watching TV on the laptop, and see if it gets near its safe maximum working temp. If not, then attaching an external monitor / TV isn't going to be a problem.
SD