You can view the content of an archived space as usual, by following a link or typing in a URL belonging to the archived space. So maybe the page the third party saw, was linked to another one.
Archiving a space also has no effect on search results of external search engines. For example, a public space will still appear in Google search results.
If all the info in the space is not important any more, you may consider to delete the space, but CAREFUL, make a backup first, as a deleted space is really gone (https://confluence.atlassian.com/doc/export-content-to-word-pdf-html-and-xml-139475.html)
The other option that comes to my mind, is to restrict the pages in question. So a third party can’t see those any more. That works like this: