You cannot camp on the riverbank. All land alongside Owens River is owned by the City of Los Angeles. If you can stay 100 feet away from the riverbank, you'll be on National Forest land, and you'll be fine.
We never saw the river at all. It's on the east side of Highway 395, so even though it's "Owen's Creek" we never saw or found the creek or any water. There are probably 100 miles of roads here though, and we only went on a fraction of them.