LEDs emit a narrow frequency band of light. Digital cameras detect color by looking at black and white luminance (brightness) sensors that go through a grid of colored filters (red, green and blue). If the frequency of light from the LED is narrow enough and doesn't match up well with the filters on the sensor, you can get odd looking color as the narrow frequency of light is largely filtered out and you only get a little bit of the edge where it bleeds over.

This is encountered a lot in LED stage lighting where you need to get special LED stage lights for ensuring good color when filming with digital cameras. The same principal applies to still cameras and single LEDs though.

As for the brightness, I doubt it is actually coming through as too bright relative to everything else, more likely, your just not seeing how much of a difference in brightness there actually is. While your eyes do have a similar dynamic range (the difference between the darkest and brightest spot) to a good modern camera, your eyes can shift much faster, giving an apparent dynamic range that is much wider. Your brain and eyes do this in the background very quickly without it really being obvious, but you rarely actually look directly in to a light source and if you do, your eyes normally narrow quickly to adjust. Direct emitted light would be considerably brighter than the surrounding reflected light in almost all cases.