No, I was entirely correct.

Your attempt to correct me is ambiguous.

I can however explain more precisely.

It may not be the website owner that owns the key, but you at least have the permission of the admin for the site to upload the file.

The json file contains a HEX converted copy of your public key, along with relay list to find you on.

Anybody can generate that hex translation, but only somebody with permission can upload it to a website.

By definition, this creates a relationship between the holder of the private / public key pair and the web site admin / owner.

In my case, I both own and administer my domain name, I can therefore verify myself.

This is a100% correct explanation and does not need your incorrect challenge of it.

This is why around a year ago, the fake Forbes reporter failed to persuade anybody to give an interview because they could not upload the hex version of their public key to the forbes.com website meaning they did not work for Forbes.

This is incredibly powerful if you think about it. Even more powerful for companies than individuals.