I think more attention must be paid to the situations where this phrase is used by the characters (main, guest, supporting) throughout the series, in all seasons. It seems to work as a clue/warning given to the audience by the writers that once a character says "absolutely", what he/she promises or believes to happen does not materialise in due course. See Christian's certainty when he tells Jack that he made the absolutely right choice in marrying Sarah, or Charlie's "absolute faith in Locke for being able to get everyone off the island, Daniel's response to Juliet after she thanked him for "helping" them, Sayid's response when he was asked if there were any other survivors of the plane crash in the press conference, Jack's response to Hurley in the helicopter when he asks whether they would come back to look for Claire afterwards...etc.
I have been rewatching the series and could not find any article mentioning the significance of the word in this sense. I think it is striking how it follows a similar pattern in each case and so deserves further attention. (If somebody else pointed this out before, apologies for repetition). Siduri