People familiar with this history get frustrated by the description you give, it is simply inaccurate. It is similar to the common misconception that the Bolsheviks in Russia overthrew the tsar, when the tsar had already been deposed months before (in the February Revolution) when Lenin returned from exile and launched the October Revolution.
Still, what is the particular frustration? Is it that other participants in that revolution don't want Iran and their revolution painted with a broad brush as theocratic? (And that would be a false image.)
It's a good lesson for anyone who wants to shift power structures: The ones who do the shifting often are not the ones who get the power.