Loft (2008)

Question: When Vincent's friends set him up, they set the scene so that the police would think that the girl drugged Vincent and then cut her wrist with the knife. But they already know the girl killed herself with the pills, or at least they think she did. At the end of the movie, female police tells Chris that the cause of death was not the pills, but it was the wrist cut. But if she really had killed herself with the pills, police would have been telling him the opposite, which would have raised a lot of questions. Were they lucky? Were they dumb enough to think that the cause of death would not have been discovered in the autopsy, or magically it would appear as the wrist cut? Or am I missing something here? Or the writers missed this?