It doesn't matter what LE is actually "labeling" her missing. They can not label it abduction if there is no evidence of it. They have to go on factual evidence.
If someone is walking down a road, a van slows down and grabs the person, pulls them inside the van and continues down the road....the "evidence" would be if someone happened to see that van and person walking in those 5 Seconds!!! No evidence is left behind, no one saw it......but it is an abduction.
Are you sure? Because I see that all the time in children where there is no evidence whatsoever what happened to them. Are you sure they can't label an adult missing/suspected abduction if there is no evidence to point otherwise?