He isn't slow. Not in comparison to anyone that isn't Sherlock Holmes. And blanket or not, he knows that Sherlock was making sense last night. So he collects the tapes from the surveillance cameras himself, and checks the timestamps, and supervises the forensics team as they go through the evidence, pushing them hours past the point where they start making mistakes. By the time he has to face the reporters he can safely say that he doubts that anyone will ever know for certain who should properly get the credit for ending the murders. Some mysteries are better left unsolved.