This is kinda out of left field but I'm really tired and it sounds good right now... Could Kelvin have been one of the others... They could have known something crashed on the island and sent someone to investigate... Then he was to make Desmond believe he was part of the DI and take post so to speak of pushing the button... Kinda so it was in the back of their heads that the button had to be pushed... Then when Kelvin was caught by Desmond he was supposed to take the sail boat back to the others?
This would tie in with at first Patchy introducing himself as DI

This could show that there have not been any DI on the island for some time... Or that the others are DI and not saying so

__________________
Please don't give up, Des. Because all we really need to survive is one person who truly loves us. And you have her. I will wait for
you. Always. I love you, Pen

DESMOND: I love you, Penny. I've always loved you. I'm so sorry. I love you!
PENNY: I love you too.
DESMOND: I don't know where I am, but--
PENNY: I'll find you, Des--
DESMOND: --I promise--
PENNY: --no matter what--
DESMOND: --I'll come back to you--
PENNY: --I won't give up--
BOTH: I promise. I love you.