Did you crawl inside to see if there were screws there?
Was the backsplace stuck to the back wall or did it look like it was attached to the deck?
When the routering was done was it just a clean cut or a bevel or ?
If there is a bevelled edge and it is within 3" from the end of the run, that would indicate it was prebuilt.
If it looks like it may be screwed down from above,, the wifes iron will loosen the glue, remove enough to find nails or screws.