Why does Albus have such a belief? He witnessed Harry kill a dementor, yes, but not control one.
That's not to say that he would disbelieve that Harry could do it, but I see no reason for him to have a reason to "very very strongly believe" it.
Because harry can carry through on his threats, and it seems the standard mental model for dementors has them being self-serving. A dementor should respond to threats, as far as I can tell.
When I was arguing this I was also taking into account that albus (and the great hall) had seen the dementor be afraid of harry, but it occurs to me that that was in the future.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: