The laws on this, as I understand it, vary from state to state. Montana for example landowners do own the stream itself in many places and can restrict it (hence private fishing areas on spring creeks and rivers). Washington law is different. Landowners DO NOT own the streambed, nor can they restrict you from being in the stream (they can block access across dry land). It is also illegal for them to string wire across the river or stream. As mentioned before, it does have to be a "navigable" river/stream, however, that definition is pretty broad and includes most all streams that don't dry up.
Deciding if a fight or argument is worth the hassle is the big decision. Most law enforcement don't want to be bothered with it.