This isn't entirely true. It's not the same intensity of flicker, but LCDs do have a small amount of flicker at about half their refresh rate to flip voltage and reduce the chance of burn-in. Also, the backlight itself may flicker depending on what kind of light source is used (especially if it's not an LED backlight, but cheap LED lights do flicker -- see christmas lights -- so it's possible some cheaper LED panels might have this effect too?).
Cheap LED christmas lights flicker because they don't have a bridge rectifier, so half of the input waveform is zero, at 60Hz. You're not going to see that kind of flicker in anything that requires real DC power (PWM frequencies for brightness control are generally way higher than 60Hz).
Some displays do this as a feature though (known as backlight strobing, motion blur reduction, etc.): LCDs take time to transition, so if you keep the backlight on at all times, you'll potentially see blurring from persistence of vision while the display is mid-transition. Instead, you can turn the backlight off until the screen has transitioned and then turn it back on so that you never show a partially transitioned image.
