There's really is a small creek which flows in the REALLY big, fast moving river. I've seen people fishing in the Kings River but not near the campground - it's moving way to fast for fishing.
Here's an article about fishing in the area. Zumwalt Meadow is about 6 miles (or 3/4 of a mile if you believe me) from the campground. I'm sure you have to have a current license.
The store at Cedar Grove sell fishing supplies as well.