I don't know the lyer river at all so i don't know if what i am going to say has any bearing in reality..

They do not own the river, That is to say they have no right to interfer with navigation on the river. If someone wants to float it and the cable caused them to wreck their boat or injure they they would be in for a healthy lawsuit. Even if the rivers is not declared navigable they cannot keep you from floating it!
If it is navigable then it is public property up to the normal high water mark and you can acess it by foot.
Remember all surface water is owned by the people of washington it therefore can NEVER be private property!!!