I believe many rivers are considered navigable, I know someone who wanted to put a bridge over a small creek (normally running about a foot deep and 5 or 6 feet wide) and had trouble because it was considered navigable
I find myself walking on the banks from time to time when wading down a river. Also people wonder what you are doing and come out and watch you sometime, I hardly ever wade on private property without permission just because it seems to bother some land owners and you can end up trespassing without intentionally doing it. I preffer to just talk to the land owner so they know why you are there.
Like others have said it is confusing so I like to stay on the safe side.