That was exactly that. I know Shatner fought hard for a reaction shot of Kirk recognizing what he just said. But Meyer chose to show Spock instead.
Kirk said "Let them die" after he just learned that Starfleet was going to be dismantled, that Spock walked over his helmet and that his potentially last assignment was dealing with the Klingons.
It was an emotional outburst, nothing more.
What I don't understand is that people completely overlook the fact that Kirk overcame his racism, mistrust and hatred against the Klingons. That was the whole point. Instead they mostly point at the let them die and then complain that it was out of character. He is very well in character at the end of the film again.