don't know about the Mississippi, but here in Arizona, the state exercises jurisidiction over any navigable waterway--by state ordinance. [even formerly navigable waters that are no longer navigable due to dams, overuse etc.--like the Salt River bed! Hence the creation of the Salt River Navy Band--you hadda be there]

Landowners only have jurisdiction over the beach.

We just had a case where one of our tribes was in the final phases of putting land into trust--and some of the land straddles the Verde River, which the state says is under its jurisdiction even though nobody has attempted to take a boat upstream since they put in two dams!! Silly bureaucrats.

Cheers,
deb