Probably because they don't want to scare him into harming the girl if he feels he's backed into a corner.
With this entire strange story, that's the only thing that makes any sense. It explains the parent's calm demeanor. It explains the MK saw the perp, but didn't see the perp story. It explains why the police are playing this story, more than I have ever seen, so extremely close to the vest.
Usually as much info as possible is out right away to try to help find the perp in a kidnapping case.
They held back lots of details right from the beginning.