I agree, though I think the charge might have been added that Chief Longo found it as a possibility to run by the DA. Longo went to law school, so he would be familiar with the charges. He said right out in an interview that it was the DA's office's decision not to arrest and charge JM when they had him both times within arms length. Not enough evidence for DA to give the "go" signal. This charge seems to fit well, by the way.
If LE has nothing more than evidence that Hannah was in JM's car, or even that they had sex, it's going to be a problem putting much of a case together against him. All he has to say is that she wanted to be let out afterwards and he did as he was asked, that any and everything was consensual. So a lot rides on the forensic evidence and whether Hannah is found, and what evidence is found on her when she is. Though, JM's behavior is erratic, I don't think it's proof positive of killing or harming her.
Jesse is already somewhat committed to the story that they parted ways after they left Tempo, as that is the story that his grandmother told the media. The grandmother could be asked to testify, and the reporter that interviewed her can also vouch for what she said.