Well, that's not how face blindness works at all. Not being able to recognize someone moment by moment doesn't impact your ability to remember their name or to remember who they are. The whole thing feels like a bad made for tv movie. The cops are charicatures reciting unbelievable dialogue.
"You don't have the right to leave me."
"I'm just another face in the crowd."
In Time might be the last movie that left such a layer a slime before this.