Trusting the old investigator's guts is the key based on his experiences, and it reminds me of when people feel like they are in danger; they have to trust their instincts to be safe.
Also, evidence is the key to an investigation and interviews to find out the truth.
Mrs. William is sneaky enough to steal the necklace and try to distract the investigators, but she is not sneaky enough with those two.
A fun cop and crime short story indeed.