I don't think this is true: many transmissive LCD technologies adjust their backlight brightness, including differently across regions, depending on the displayed image?
OLEDs incorporate the backlight with the pixel, so they can turn on or off the light for each pixel, giving you much nicer blacks. A typical LED backlight is just a single uniform light, so it can only be adjusted for the entire screen, and unless your screen is black, you need some light. I guess if everything was a at most a darker grey, they could crank it down, but I don’t think anyone does that?
I'm not sure about typical, but I believe most high-end LED backlit displays use at least one of global or local dimming of the backlight depending on what's on the screen.
This means that the power use of this type of LED backlit display is also sensitive to what is being displayed (but at a coarser resolution to OLED).
