I'm no expert in biology, and biology may describe this phenomena? I am applying what I know about physics.
Sunburn is caused by excessive exposure to skin-damaging UV light.
I tend to believe that wet skin by itself does not cause you to burn faster, one merely feels cool in water, so one is prepared to stay out in the sun longer. I can't see any reason for why wet skin would amplify the effect of burning (barring localized droplets, possibly causing what I will call "spotted sunburn"). In fact, some frequencies of UV are absorbed by water, which would seem to reduce the effect (by how much, I'm not sure). In fact, having a layer of water on your skin would seem to help reduce sunburn (however slightly) because some of the UV will be reflected by the water.
That being said, consider a large body of water. Here are a couple of situations you might find yourself in:
If you have your body submerged in water it is possible that more UV could strike your skin due to the water surface not being flat (a lensing effect).
If you are above the water (for example, on a boat, or just your head and shoulders poking out of the water, etc.) there will definitely be more UV striking your skin, due to there being not only direct light from the sun, but reflected light from the surface of the water.