Wow. Very red. I doubt that red would photograph as strongly under artificial lighting (strobe or video lights) because it looks like a fluorescent red too me. In fact, with flash I would expect it to look just like Tim's shots, above - a reddy-brown colour. Indeed, I would not be surprised if it is the same individual as in Tim's shots.
Shooting in ambient light underwater tends to exaggerate fluorescence, e.g. glowing red anemones, red algae in the UK, fluorescence corals etc:
http://wetpixel.com/...showtopic=10016The effect is further enhanced if shooting with a filter. Basically the blue colour of light at depths acts an an exciter wavelength for the fluorescence and the on camera filter acts as a barrier filter for the ambient light on reaching the camera, allowing the fluorescence to be seen.
This is why when you see a glowing red anemone (such as the one at small crack in the Red Sea) and photograph it with flash you don't get that glowing red colour you remember. If you shoot it with ambient light and a filter (usually on video) you get an even stronger red.
I believe that is why your occy looks so red. So what is really fascinating is that the blue-ring seems to have some fluorescence on it. Which octopus do not normally have. This red fluorescence is very typical of algae, suggesting to me that this octopus has algae on its skin. Which raises lots more questions...
Alex