If the spectrum of the LEDs match the sensitivities of the eyes, then everything is fine. But LEDs are narrow spectrum; they won't reproduce color the same way as a broad spectrum light source will.

As for LED screens, those are emissive and work great for simulating any color. However, they are not good light sources for lighting objects because they're narrow spectrum.

If the object you're lighting up is broad-band reflective (like paper with broadband black pigments), then everything is good. But as soon as you get narrow-band pigments, colors are going to be distorted.