Just goes to show many gamers do not infact know what "input" lag is. I've seen the response time a monitor adds called input lag way to many times. And that mostly doesn't in fact include the delay a (wireless) input device might add, or the GPU (with multiple frames in flight) for that matter.
seems pretty pedantic. the context is monitors, and it's lag from what's inputted to what you see. plus especially with TVs, input lag is almost always because of response times.
Lets see If I get this right, input lag is the time it takes from when you make an input (move your mouse) to when you see it happen on screen. So even the speed of light is at play here - when the monitor finally displays it, the light still has to travel to your eyes - and your brain still has to process that input!
Once I tried playing Halo or Battlefield on a friend's xbox with a wireless controller on a very large TV. I couldn't tell which of these (the controller, the tv or my friend) caused the delay but whatever I commanded happened on the screen, like, 70ms later. It was literally unplayable
My guess would be the TV wasn't in 'game mode'. Which is to say it was doing a lot of post-processing on the image to make it look nicer but costs extra time, delaying the video stream a little.