"Yes," said Dumbledore, as he descended to the bottom of the dark stone stairs. "Let us all go home, indeed." His blue eyes were locked on Harry, as hard as sapphires.

It suddenly occurs to me that Dumbledore has seen two interactions between Harry and a Dementor. In the first one, it almost destroys him. In the second, he casts a Patronus that destroys it. Neither would seem to provide the kind of evidence that you would need to confidently assume that other Dementors would run away from you if you said "Boo" to them.

So, is this enough evidence for Dumbledore to decide that he's wrong about who broke Bellatrix Black out of Azkaban?