TLS has very little to do with it. Some intermediary parties may be able to read the plaintext, but that's different from putting it on pastebin for everyone to see. I've never heard of ISPs or transit providers publishing privacy-sensitive data or otherwise snooping on it. (Assuming non-business / non-VPN / non-proxy connections. Just an ordinary internet connection.)

The author probably meant if the site gets/is hacked, or if they are later bought by another company, or if a new employee joins and you can see chat history... etc.