Was the unacceptable proposal something illegal or sexual in nature?
If they know she went to a bar, and then later to the suspect's house, and that the suspect made an unacceptable proposal- in that level of detail, then they know who killed her, right?
No details whether it was illegal or sexual. Actually, if they think the murderer is such a psycho watching the investigation in the crime scene from a distance, I don't think they would share this much info with the media.