Yes—some LED photo/video panels can be effectively flicker-free for stills and video. LEDs themselves do not inherently flicker; flicker comes from how they are driven. If the light uses a stable DC constant-current driver, it may show little or no visible flicker, even at fast shutter speeds. If dimming is done by reducing current rather than with low-frequency PWM, it can remain flicker-free while dimmed.

That’s different from many cheap household LED lamps, where simpler electronics or PWM dimming can cause visible flicker or banding.

So your result is plausible: a lighting panel designed for photography/video may genuinely be flicker-free, or flicker at a frequency high enough not to show at 1/4000s in your test. Your method is a reasonable practical check, but it only proves that no flicker was detectable under those conditions—not that every LED light is flicker-free or that flicker has been “eliminated” in general. Flicker is a property of the power/driver setup, not of LEDs as a category.