I understand the points of the case, I wasn't trying to include or omit details. My comment was about circumstantial evidence being a valid basis for conviction, I never realized it was. Has that always been the case? (no pun intended)
To prove who committed the murder (after proving that the person's death was a homicide at all), all you need is to exculpate two of the three remaining people (by e.g. having them supply air-tight alibis.)
Then, by process of elimination, the last one must be the murderer. Even though that's entirely "circumstantial evidence", it really is a proof, in the deductive sense.