Why are recovered flight data recorders kept in water?

They do this with all components that they wish to salvage out of drowned aircraft. The very instant that you remove submerged components from the water they start to corrode. It better to keep them in the water until they get to an inspection/repair facility where the can be transferred to a corrosion inhibiting media. After that they can be taken to the workbenches.

If it was recovered from under water, letting it dry out could damage the recording so that they couldn't read it at all.

There are ways to safely recover the recording without damaging it, but it has to be done in a controlled manner.