In most places it's a contamination and overuse thing, but that's not a stone hard rule and here in the Ozarks/Ouchita Mountains you can camp on the banks of many popular canoeing/kayaking streams. You're required to be a few hundred feet from any water source to relieve yourself though. And you're advised to be aware that flash floods can and do occur so you should at least have a fast exit to higher ground if you do camp near the water's edge.

The reason it's not an issue on some streams here is because those streams rise over their normal banks several times a year and any trace of a campsite disappears when they do, and the only trace you'd find before that happens would be footprints and the remnants of a campfire. Occasionally, campers get washed away with the high water too.

I look for gravel bars that are at least 10 ft higher than the water level and have access to a steep, but easy to climb, hill behind me, and I pay close attention to the weather forecasts and weather radar from NOAA.