Your conclusion is remarkably logical, but I think you are getting a little side tracked by the fact Nero and Co are such a nasty bunch of villains. I mean, would it be OK to "help it along" if the people on the Narada were in the same situation but innocent of any crime?
I'm thinking not. So there is something a little dodgy about the principle that it is OK to kill someone (especially when at your mercy) if they are going to die soon anyway. Interesting ethical point though.
Their guilt isn't really a factor in my thinking. Obviously if Nero is prepared to accept their assistance, then they're obliged to provide it. But he isn't:
I would rather suffer the end of Romulus a thousand times. I would rather die in agony than accept assistance from you.
Given Nero's situation, his death is inevitable without outside assistance. Assuming that his co-operation is required for that assistance to be provided, there is no helping him so long as he feels the way his lines there indicate. Since assisting him will almost certainly mean at least dropping the shields, and since it's reasonable to assume that at least some of his weapons remain both online and operable by him, there is no reasonable path open to Kirk that ends with rescuing Nero. Hence the deaths of Nero and his crew are inevitable and hence my indifference to the firing.
If the ship were crewed by a posse of fanatically suicidal innocents who are willing and able to prevent their own rescue, I still see no significant ethical distinction to draw between watching it happen and hurrying it along. It all hinges on the feasibility of forced rescue. If you can persuade me that they could have forced Nero or some of his crew to be rescued without exposing the Enterprise to grave risk, I'll have to change my mind. On the other hand, if you accept that their death was inevitable, you have some work to do to justify distinguishing between watching and firing (IMO at least).