I agree with both sides of the argument up to a point. Each view is valid because Trek has always been inconsistent. I enjoyed the movie immensely even though some elements (the long distance transporter being the biggest one for me) I found profoundly irritating.
My personal view would be that Kirk offers assistance, Nero rejects, Nero (like Maltz) tries to take Enterprise down with him, the gravity of the singularity pulls his own weapons back and his own hatred destroys him. It makes sense and sends a more powerful message to the viewer. Actively wasting time at the edge of an expanding singularity was a poor tactical decision whether you approve of their actions or not. It makes it much harder for me to credit Kirk with the sense to be a captain at such a young age.