You might be mistaking my intent. I bolded the line in your quoted comment to point out the line I felt was pertinent to my point. It was bolded to aid understanding, but since that did not work...
It is very easy to lose someone once they are overboard.
A mile is a long distance (further than one can see a man's head
bobbing in the ocean), creates a large search area, and despite it being a large motor
vessel, which presumably can travel at any speed it wants to go (unlike a strictly sail boat), and in any direction it want to go, it may take a while or relatively long time to FIND the MOB
if they are searching visually for a small object like a man's head
among the waves.
Put another way, if the helo had not arrived, that guy might not have survived, if depending upon his boat to find him.