Squid fishermen use really bright lights (which can be seen from space!) to attract squid to the surface at night, but a lot of squid also naturally avoid surface waters that are lit during the day (by the sun) and at night (by full moon). As far as squid are concerned, what is the difference between the bright artificial lights and diffuse light that naturally occurs?
Despite many sources stating that the lights attract the squids, the explanation given here is much more logical. Squids feed of small fish, crabs and shrimp, which in turn feed on plankton. Zooplankton is known to migrate vertically during the day (up at night, down during the day), which has also been reported for squids, probably following their prey.
The reason for this migration is that zooplankton feeds on phytoplankton, which can be found at the sea surface, where it gets most of the sunlight. During the day they zooplankton stays in deeper waters, because at the surface its easier to be spotted by predators. It's safer to move up during the night to feed. Other predators feeding on zooplankton follow, including the squids.
The vertical migration might be coordinated by an internal clock rather than light. It would therefore not be inhibited by the bright fishing lights. The squids don't seem to respond to the light, but rather to their prey.
Therefore, rather than attracting the squids directly, the fishing lights will attract phytoplankton, which attracts zooplankton and small fishes, which attract squids.