Lighting for octos is more about what makes the animal comfortable enough that it doesn't hide all the time than anything else; bright lights won't damage it directly, they just might make it stressed out, reluctant to eat, and so forth. Since most people want their octos to be "out and about" as much as possible, we tend to recommend lower light levels than most people use, and not to mix other animals or plants that do have specific need for bright lights into the tank.
This depends a lot on the species of octopus as well; bimacs and cyanea tend to tolerate lights somewhat, while a lot of the pygmies are completely nocturnal and will never come out unless it's very dim. Usually, moonlights are too bright for these, even. As far as I know, no one has demonstrated that any lighting is directly bad for octos, although I worry about strong UV lights a bit, since it seems likely that in their natural environments they're somewhat protected from UV, so bright UV might damage the skin, but that's just something I wonder about, not that's been proven.
Octos, as far as has been studied, don't see in color, so really the main issue is "does this look so bright to the octopus that it's uncomfortable?" The visual sensitivity of an octopus is somewhat different from humans, so there are things that look pretty bright to us that look dim to an octopus, and things that seem fairly dim to us that the octopus is very sensitive to. Octopus visual pigments tend to have peak sensitivity in the blue-green part of the spectrum, which makes sense, because in the water most of the red and yellow in the spectrum is filtered out once you get to a depth of more than a few feet. Because of this white, or blue-white, or purple-white lights will tend to look a lot brighter to an octopus than to a human, so octopuses that prefer to wait until dark to come out will often see all 3 of the lighting schemes as "too bright for comfort." Moonlights that are on a dimmer so that you can find the level your octo is OK with are one approach. Another one, though, is to use light that's more in the red part of the spectrum, since this will look much more dim to the octopus than it does to a human. Red LEDs seem like a good choice for this sort of thing, because they tend to produce a lot of light in a part of the spectrum that humans are much more sensitive to than octos, so they allow you to see your octo, but your octo isn't terribly nervous.
Most octos that end up doing well as pets, though, tend to become comfortable with enough with the safety of their tanks and inclination of their keepers to feed them rather than attack them that once they are comfortable, they come "out and about" regardless of lighting... mostly, we just try to point out that a lot of reefers and fish keepers like to have very bright lights to highlight the bright colors in their tanks, which is not the lighting octos tend to be comfortable with in the wild-- even the diurnal ones tend to be out more at dawn and dusk than when there's bright sunlight, so people used to keeping their tanks brightly lit 24/7 will tend to have octos that hide and are stressed, and if you're setting up a tank to primarily be an octo-tank, it's not really useful to spend a lot on fancy lighting.
Also, just for completeness, there are a lot of octos that really don't like camera flashes. Some get used to them, but some never do, and will run and hide whenever they see you coming with the camera as a result...