claiming a boat completely disappears right in front of them 3 miles out.
Only you and notbatshit are claiming that. The curvature adds an ~8 inch drop per mile, so it would have to be a very small boat (~50 inches) and your eyes/camera would have to be at the water lever for it to go beyond your horizon in 3 miles.
A more realistic distance is 10-20 miles depending on how tall the boat is and where you're standing.