His T-800-like obsession actually echoes the last words of Superman, asking Lois about Doomsday. It makes sense that if Superman came back with little memory that his first order of business would be to rid the world of Doomsday once and for all. Henshaw was very good at establishing trust.
For those too young to remember, “The Death of Superman” was a huge storyline with major mainstream news coverage and it was possibly the first storyline where the main character actually died. Sure, characters died, you lost Uncle Ben, Gwen Stacy and Bucky but you never lost Spider-Man, Captain America and certainly not Superman, the greatest hero of them all!