This is a good question for legal minds and my mind is not one but here is what I do know.
I have bought land and owned both sides of the creek. I had the rights to the creek but not the water as it affected neighbors downstream. Therefore I could post both sides of the creek and control access. I have bought land where I owned to the middle of the creek and only controlled to the middle of the creek and just posted one side from tresspassing.
Now my understanding is that if is a navigable waterway meaning boat ,canoe,kayak you can not stop people from traveling down the creek. But this does not give them permission to Hunt wildlife and if it is posted they must have written permission to hunt. I do not know about removing artifacts which may be deemed their real property. Ughh.
For instance the wild life resource agency contacted me for permission to stock trout in one of the creeks that I control that runs for several miles. I said sure what is the catch. They said I had to open it up to the PUBLIC. I am thinking injury lawsuits etc. so called my insurance agency and they said no way do not open up the creek to the public as we can not cover that.(Loyd's of London will though).You can buy a 2.5 mil policy and let people wander everywhere .

So my guess is someone somewhere owns the creek to some degree. I know I walk creeks but most times know the owners of the lands that I am on. It is not much diffrent than hunting a plowed field,,,
I think you may have more rights on what they call a navigable waterway with a boat than walking on a shallow gravel creek. Navigable is going to be a key word.
Am sure this is not what people want to hear and most times landowners are pretty easy to get along with but get a few that have been run over and I mean abused by people trespassing and my bet is you would loose in a court of law if it got that far. Each state is diffrent on posting laws. Here in Tn we must post every 100 yards on a boundary line. In Ala you can paint the line blue and it means the same thing.
I would try to check your STATE LAWS. You can not tell these landowners they do not own the creek when a legal deed puts that creek with in their property lines.
I do work for a land office that deals in large tracts of undeveloped land and carry a professional lisc plus I manage over 4000 acres and the many rights associated with those lands.
But this is a humble opinion and one us artifact and metal detectorist must deal with when venturing out for our hobby.
Good luck and hopefully someone with some type of degree in this will weigh in.
HH
