Photographing Ultraluminous LED-lit Art Projects

http://web.mit.edu/neltnerb/www/artwork/index.html features artwork
illuminated by super-bright LEDs, but the photos do not accurately
reflect the colors of the lighting. The artist says that his camera
has trouble picking up the purple lighting, instead showing it washed
out, apparently because it is outside the normal color space of the
imaging sensor. Does that sound likely? What might a photographer do
to take better photos of these tricky lighting situations?