In discussing this at the theater this weekend, my sister said she remembered a story where it looked as if a robot had murdered its master, but I couldn't remember one. I looked through story summaries, and I remembered most of them but still couldn't find one like that.
I finally ran across the Wikipedia entry for the movie, and it all came together.
- The screenplay was written before they took Asimov's title!
- There was already a good faithful screenplay written!
For all I know, it's a good movie. Unfortunately, being saddled with the name of a great book means it has a lot more to live up to than if they'd just kept the original name ("Hardwired"). I don't see Bridget Moynahan as Dr. Susan Calvin, but she could have been fine as some similar character in a movie with its own title.