First off, to answer the original question: No, he should not have saved them if they were unwilling to cooperate. Trying to get them off the Narada while in an uncooperative mood would have risked Kirk's own ship and crew. If they're willing to cooperate, it's your duty. If they aren't, and their lack of cooperation endangers your crew, save your crew.
As for firing the torpedoes -- place yourself in Kirk's position. You have stated that the vessel is compromised, but given what you've already seen and lack of familiarity with an obviously advanced ship capable of killing billions, do you KNOW that? Do you take the chance? Logically, you don't. Whether you get that crew off or not, you're going to make DAMNED SURE that ship is destroyed.
As for Spock's argument, I think you can impose whatever meaning you want. Perhaps Spock has momentarily given himself to the Dark Side, or he's the same old Spock who is eminently logical. There is no time to rescue the Narada's crew and jeopardizing the E's crew in the effort is a needless (and therefore illogical) risk.