Just looking through my log files today and I saw for the first time that when someone found my site from google, google media bot hit the page not more than 10 seconds after the first GET from the visitor. This appears new to me or else I didn't notice it before. Is this something new that anyone else has seen, or is this old hat? Idon't know if there is any significance to this, but thought it was interesting.
There are quite a few ways for Google to find out that a particular page is visited by someone and occasionally this may prompt them to spider that page. It has been well known for many months that if you visit a page using Opera with the Google adbar in it the media bot will often follow in a few minutes. I wonder if the phenomeon that you tell about is basically a result of the same strategy?
The mediabot has nothing to do with the main index either, it just tries to understand what a page is about. 10 seconds is quite slow for mediabot, I have tested stuff before and have seen it immediately appear when a new page is asked for.
I wouldn't worry about this, it's natural (unless you don't have adsense on the page!)
There's no need to think how you can exploit this bot either, you can't.