I am going to a spot where there was a big battle. I am in a state where the owner has no right to kick someone off of the creek that runs through their property. should i detect?
All such "national parks", will be indicated by color code, as to their borders, on a map I would think. And if your zone is outside of that shaded color, then presto, it's not "in" the park. Dunno why the word "near" would have anything to do with this issue. If someone doesn't like it, they can just go pound sand. As long as you're not in their "national" zone, then ..... they can pound sand.
Most states follow federal law when it comes to property rights regarding navigable waters...in short, if it is a creek that normally holds enough water to canoe or navigate by boat, then it falls under the category as "navigable," thus should the owner of the adjacent property thinks that he can exclude your or anyone else, he would be wrong. It's usually more complicated, but that's the common law in most states.
So in other words laws don't automatically "subrogate downwards". For example: If a particular state had "no md'ing" wording in their state parks statutes, then those don't automatically subrogate down to county and city level parks. Because state parks are different than county and city administered parks. They are two separate beasts. Same for federal vs state.
In the same way I don't think that federal laws regarding navigable waters necessarily subrogate down to navigable waters that are not *specifically* federal property.