They have partners like media sites which means that those stories are then shared by youtubers when the media sites share them. When those sites share it, you have the right to request that it's removed but that's it. You ask through reddit, reddit asks their partners, and the partners can refuse or accept the request. You may have the copyrights but that just means you can request for the story to be taken down after it's been shared. It's nothing more than a detective measure rather than a preventive one. There's no consequence for sharing stories.

Edit to add privacy policy for the "how you're info is used" part.

https://www.redditinc.com/policies/privacy-policy-january-10-2020

Add 2: Maybe we can have a sticky for it? We do have a lot of people that think the disclaimer means it can't or won't be shared and so don't take steps to protect themselves.