". If so, my question then is, what gives someone the right to claim the water that immediately surrounds his"
Wow, ignorance is bliss.
No one claims THE WATER around their mooring. However, a mooring is sunk into the bottom and bottomlands are regulated very differently from navigable waters. Sometimes the bottomland was assigned by Crown Patent, and that survives in the US today as private ownership. Sometimes the state or municipality owns the bottomland, and has made arrangements to lease or rent our mooring rights.
How can you... (Edit - Infammatory and Unecessary - tdw) You really have no idea that all land is OWNED in the US? Really, you' better do some research on your own state and theneighboring ones, because the laws vary in all of them. But no one is allowed to claim ownership of navigable waters--and that term is federally defined too.
You might want to read the Coast Pilots as well, because if you just drop anchor
in a regulated mooring field, the local watercops AND the Coasties will send you tickets to the policeman's ball.
Why can't I park my car on the White House lawn? Or, on the Capital Mall? No, really....
Why do so many people even think they can just go where they please? And bring a boat with them?