"What in the world would I need as far as
documentation from the owner so that I ACTUALLY
own the boat after paying for it?"
Your best bet is to contact the USCG Vessel Documentation Center directly, they can tell you what is required to register/title and/or document the boat in the US. There is specific paperwork that is and is not acceptable.
Similarly, you would need to contact the embassy for whatever country "your" purchase is located in. As a non-citizen of that country, you may not be able to get the equivalent of documentation. But whatever you can get--you'll want to confirm it directly with their authorities before you go. If you are dealing with an established brokerage, they may be familiar with it--but verify it directly.
You wouldn't want to find out you'd bought a boat, sailed it home, and then someone filed a title lien on it because you didn't know something, right? And, coming into the US from South America...wouldn't you really rather be SURE the USCG was going to let you in?
Back on Johny's topic...
is the actual visa application form for visitors coming to the US. Among the questions are who will pay for your trip, where and how long are you staying, who is your employer or school, and have you ever been convicted. The actual criteria are not listed, but I would suspect that if someone said "Well, I'm not really staying anyplace, I'm not staying with anyone, and I'm not employed" they would say no visa.
And that's actually the global NORM. For big nations and small ones. Flying or sailing IN and planning to hoof it out? Many will require some kind of proof that you're financially able, or that the exit ticket is prepaid regardless of whether you use it.
But when you don't have specific answers for the visa application questions....Uhuh.