It probably wouldn't have mattered even if they had found the horse. He would have been beaten for trying to hide it. Hell, Jesus sometimes got hit even when he handed his things over. It's part of what had made him decide to learn to fight back: if he was going to get hit no matter what he did he wanted to hit back.

But that's not K, who takes the beating. Even now.

"I thought they gave you memories to make you stable." Nothing about growing up in an orphanage makes a person more stable.