@XulChris: they are not “owned” per se, rather they are like a “no mans land” that is put under the stewardship of the states or the federal government. Rivers that cross state boundaries are regulated under the commerce clause. And I quote from Wikipedia “The commerce clause provides comprehensive powers to the United States over navigable waters.” read more here -> http://goo.gl/HAkxw
Even when rivers abut land that one owns you do not own that part of the river, rather you are required to grant an easement to it and thus lose all rights to it (like homeowners that must grant an easement to the government for any road that passes by their property – so that homeowners can not erect tolls or otherwise obstruct passage. The only way I think a private person could own a river is if it went in a circle within a single state and you own all the surrounding land. Is it impossible that there are any privately own rivers (as in not required to grant easement rights to the state)… no… but given the power of the federal government with respect to its authority over navigable waters I highly doubt it.