Bleak, fish can see without a divers mask. It would easily be able to see a red Jan sitting on the bank.
The reason why tackle say it becomes invisible is because as it says in the article the longer wavelengths of light get absorbed quicker in water. For humans the normal visible colours are the colours of the rainbow with red having the longest wavelength and violet having the shortest.
This means that in clear water the further you go down the less light there is but there is proportionately less red light sooner than violet. The line has not become invisible or colourless instead it would look black to a diver with a mask or a fish.
Most leaves of terestrial plants are green, this is because the green light is reflected and all the other wavelengths can be absorbed and that energy is harnessed by the plant. ROYGBIV. The colours of the rainbow. You will notice that green is in the middle, that allows the plant to be able to absorb as much energy as possible under lots of different light conditions. If you live near a part of the coast with a large tide at low tide you will notice that a lot of the plants will be red. This is because they reflect the red light that won't reach them any way but are able to absorb the green light (and blue etc.) that will travel further through the water.
Jeff, some species of fish can see ultra violet. I can't remember off the top of my head which ones. It would be simple enough to design experiments to find out but it would take a bit of effort to do it in free (or as we call it "fishing time") time. I'll try and look up some articles over the next ten days and come up with something better.
One thing in the article that Waggy put up was the fact that murky water or water with plankton sometimes reverses which wavelngths permeate furthest. I have my favourite lure colours in different conditions but this might give me something more tangible to work with rather than I have a liking for this or that, especially when my fishing buddy has the exact opposite feeling.