Not alot of knowledge on this FF but I have quizzed game wardens from both TX and OK about the red river, Peas River and Guadalupe.
On the Red River, it is Oklahoma territory from water on Texas side to "high water brush line" on the OK side.
By Wichita Falls on the Peas and Guadalupe, You can hunt the river bottoms up to the "high water brush line". Private land starts at the perminant brush line and the river is public access. Not the water but the whole river bottoms. There are some big ranches around there and they protect their property with lethal force.
The game warden from that area informed me of these boundaries while standing in the river bottom. I was leaving with a rifle to go whitetail hunting.
I am not sure of how far up a tributary you can traverse while still being on public access. I will ask next time I talk to one.
Just because you know the correct answer, that doesn't mean the land owner knows. YOu may get shot anyway.