Contacts unexpectedly added to group
I can think of three reasons why this would happen.


"Board Members" is a smart group.  You can check this by going to Contacts menu » Manage Groups.  If it's a smart group, it either a) shouldn't be, or b) the criteria need to be changed.
The Board Member group is the parent of some other group. I did this by accident myself recently; you'll need to remove the parent-child link.
Some custom magic.  If you're the only administrator of the database, we can rule this out.  However, I perform similar tasks all the time, either using a) cron with a SQL query, b) the SQL Tasks extension, c) a custom extension.