Yeah basically.
I just wonder how people would've salvaged it, or what they would have done. If you were going to go back in time and wave a magic wand to change one point, what would the point that fixes everything be?
The poster above is correct. You start the game AT the murder, or it is the first scene where anybody has an opportunity to do anything other than speak (exactly how this sort of thing is handled in film).
Some ideas for after-the-fact salvaging:
The Player finds out they were wrong, and failed to kill the NPC. Two versions of this one:
1. Switch the murder and the victim's ID's. So in this case, the dead NPC was the target all along. Upon examining the body, it is discovered they were already doomed before the PC became involved (poison usually works here), and whatever the PC did simply sped up the process by a few minutes.
2. The NPC did NOT die, despite what the PC believes. The believed-to-be-dead NPC frames his would-be murder for the actual death of whomever you had originally planned.
Before the incident, you could have prevented the death easily. PC's don't simply succeed at everything via declaration. When the player announces his intent, mention others are close by and could hear or see, describe the NPC as being physically intimidating and give the player the impression they may not be able to take them out.
It's impossible to tell you what you could have done differently without knowing what exactly happened. Where did he kill him? How did he kill him? Did you know he was going to harm him?
Also, sorry if I missed it, but did you say the group knew this was a Murder Mystery? What kind of RPG were you running? Horror? Fantasy? What?