Do any fish have to hold their urine in deep water?
In a salty environment there is the risk of loosing water by osmosis.
There are different strategies to prevent this.
One of them is to hold the salts of the urine (not the urine itself) by reuptaking them from the kidney.
The resulting high internal salt concentration prevents the water loss.

This strategy is used by Sharks and rays/ skates, they take up urea and TMAO from the kidneys. Those metabolites are highly concentrated in their blood, which makes them unhealthy to eat, when fresh. However, after fermenting they are edible: Hakarl is an icelandic dish of fermented shark. The linked Wikipedia-Article gives more details about the topic.

I guess your friend was referring to this phenomenon, but his memory was a bit imprecise.