A baby cannot be left unsupervised. If he needs to be somewhere he can't hurt himself, consider a pack n play or a crib. I don't get how he thinks allowing a 13 month old to toddle around without someone actively watching him is a Good Idea. I think it's a very Bad Idea. I think your DH is upset because it was a selfish plan on his part. "Go nap...but I'm not going to watch the baby, either." Grow up and be a parent.
When my DD was 18 months old, in the kitchen WITH me, she quietly got up on something, got tacks off our board and put them in her mouth. I spent 3 hours in the ER waiting for the xrays to see if she ate one since a perforated stomach is a bad thing. She was OK in the end. Had I been sleeping? I doubt it would have gone so well.