The amount of color shift depends on how much water is between the object and the camera, so you need to have a depth map to recover the true colors. You can see how it compares to naive color transforms in the paper.
Isn't the blue shift of a known color already a measure of the amount of water between the object and the camera- and therefore its distance? Knowing the true color of a fish, a seaweed or the sand isn't already enough to infer distances and color-correct?
(1) often with pretty bad results, but consider the variety of scenes and object above water compared to the average underwater scenario.
I am pretty sure that in most cases those colours are well known.