So Server Beach has an automated system that detected copyright infringement in a "cache" file and automatically shut down the server before checking to see if it was actually visible to the public (which according to the article it was not)?
If content is visible to your dedicated (not managed) hosting company, who doesn't have any login access to your servers, then yes, the content is visible to the public. Access to it may be obscured, due to removed links to it or however it was supposedly 'removed', but still available to the Internet and henceforth public.
The hardest part of climbing the ladder of success is getting through the crowd at the bottom.