Problem with Google indexing a PDF on an allegedly "private" child blog

Greetings,

We have a problem with a user of one of our blog network... Here's want happen :

The guy created a child blog on our network, uploaded a PDF document. Later on he deleted the website. In the mean time it seems that Google indexed said PDF document. And now he's quite angry at us.

IMHO, the most probable explanation is that he made the website indexable by search engines for a while, and that's when his PDF document was indexed by Google.

Please note that on our blog network the child sites are NOT indexed by search engine by default.

A few questions to you guys :

1) Do you agree with my interpretation ?

2) Assuming he didn't change the default setting to put his site into "index mode", is there a way the PDF was still indexed ?

3) In your opinion, could it be a bug in our blog network, or is it more likely a human error from the user ?

4) What would be the best way to remove that content for the student (my guess would be to locate and remove the file on the FTP if it's still there, and in any case do a Google removal request via Google Webmasters Tool).

Please let me know what you think, thanks a lot in advance for your insights. :wink: