that is kind of interesting and, if true, does seem fishy. But then again iranians don't necessarily vote along ethnic lines and mousavi doesn't necessarily enjoy any particular popularity amongst azeri. I wouldn't like to say definately the election was totally above board, i don't think many elections anywhere in the world are completely fair and square, but i am still not convinced.
As to the idea that the real power in iran is not held by the president or the members of parliment but rather by the guys in 'nice hats' is much to simplistic and actually not true. You could say the same of the US that the real power is not held by the president, senators and so on but by the trumps, rockerfelleres etc.. and it would probably be more true.
Iranian politics is more complex than that. Definately there is a high degree of sincere devotion to the main religion in Iran and that certainly gives the clerics influence in that what they say and think and write is given serious attention by civil servants, elected officials and the public alike. But that is not really the same as some kind of secret machievellian dictatorship. Consider this; one of the four candidates in this last presidential election was a cleric (ie one of the guys in the nice hats) (and a reformist candidate at that!) mr kharroubi and guess what? not only didn't he win he had the least votes of all the candidates...
Okay okay i can hear you thinking but what about khameni isn't he supreme leader? Doesn't he have a 'nice hat' doesn't everybody have to do what he says? The supreme leader has a formal position similar to that of the monarch in british politics which is to say head of the state religion, head of the armed forces and head of government. But like the british monarch in practice what this translates into is a sort of team mascot, a figure head, who has some influence according only to his abilities to persuade those with actual power but not more than that.
Actually in formal terms the supreme leader has rather less power than the british monarch because unlike the british monarch he can be fired from the job and his children don't get any right to take over the position after he perishes.
In practice the supreme leader does offer advice and exert influence a good deal more than the british monarch has (at least in recent times) and he is listened to but there is no mysterious dictat forcing obediance... just as often his advice is politiely ignored...
Of course other organs of the state don't have any absolute power either such as the civil service, president, ministers of parliment etc. Rather iranian politics is a soup of commitees, agencies, councils and other positions with diverse people with differing opinions on what should be and how it should be done who try and persuade and influence things as they see fit, sometimes for their own selfish wants, sometimes for the greater good. Really rather like the politics of any democratic country.