This was in Colorado. Apparently, if someone owns the property on both sides of a river in Colorado, he owns the land under the river, too, so don't be wading on it.
That's true. It's the same for Oklahoma.
There is also a program in Colorado with their wildlife department that pays for stream bank access along the banks of streams and rivers. You can walk as high as the flood line across private property if they are in that program. The flood line is basically where driftwood has drifted at the peak of the flood and the river/stream receded leaving the driftwood.
Walked many miles along streams using that program in Colorado. There are some hold-outs though. Several of the trout clubs lease vast stretches of the best streams for their club use only.