The Blogs of the Day (BOTD) internals are a trade secret. Plus, I have so much fun reading your hypotheses and I would hate to ruin the fun!
I can let you in on a few things, though. BOTD does not use your blog stats; it has its own counting mechanism. The lists are regenerated every hour from the last 24 hours of data.
The featured post (Blog of the Minute [BOTM]) is usually the #1 post in whatever language you have selected, but we have a way of overriding that whenever we find something worthy of notice.
You can see the rank of a post in the list by hovering over it or viewing the source.
At some point we started sending pingbacks to all of the top posts in the Unfiltered list as it stands at midnight UTC.
BOTD used to be powered by a WordPress.org installation but it is now a regular WordPress.com blog. (You might have noticed when the admin bar started to appear there a few weeks ago.)
Hmm, what other beans can I spill? I think that's enough for this year. ;-)