(4 squares/move) for the PCs.
Are you playing 4.0?
the water is kept violently in motion by the power of the (spoiler)... It costs 4 squares of movement for wading characters to enter a square of churning water, and tumbling is impossible.
I know deep bogs cost 4 squares of movement, so it didn't stick out. Does it make a difference?
Yes, a creature with a swim speed could take a 5-foot step in "choppy water" terrain, by core RAW. (This is probably covered explicitly somewhere in Stormwrack, and I wouldn't be surprised if the answer went the other way.)
That said, if I were playing a swim-speed PC, and you as DM told me, for example, "It's difficult terrain because it's water, and it's doubly difficult because the water is choppy, so it counts as difficult for you; the choppiness affects you but the depth of water doesn't," I'd find that perfectly persuasive.
You can only take a 5-foot step if your movement isn't hampered by difficult terrain.
You may not take a 5-foot step using a form of movement for which you do not have a listed speed.
In some situations, your movement may be so hampered that you don't have sufficient speed even to move 5 feet (a single square). In such a case, you may spend a full-round action to move 5 feet.. . Even though this looks like a 5-foot step, it's not, and thus you provoke attacks of opportunity normally.