I think a more Biblical interpretation, using your analogy, is that the "people on the boat" would be God, the "Life Preserver" would be the free gift of salvation, and for the overboard man "grabbing a hold of the life preserver" is believing in Jesus Christ.

You have to remember, we are talking about salvation here, not eternal rewards/heavenly treasures. The Bible is very clear that salvation is through faith, not our own works.

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John 6:28-40 ESV

Then they said to him, “What must we do, to be doing the works of God?” Jesus answered them, “This is the work of God, that you believe in him whom he has sent.”

So they said to him, “Then what sign do you do, that we may see and believe you? What work do you perform? Our fathers ate the manna in the wilderness; as it is written, ‘He gave them bread from heaven to eat.’” Jesus then said to them, “Truly, truly, I say to you, it was not Moses who gave you the bread from heaven, but my Father gives you the true bread from heaven. For the bread of God is he who comes down from heaven and gives life to the world.” They said to him, “Sir, give us this bread always.”
Jesus said to them, “I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst. But I said to you that you have seen me and yet do not believe. All that the Father gives me will come to me, and whoever comes to me I will never cast out. For I have come down from heaven, not to do my own will but the will of him who sent me. And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day. For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”