Here are the facts:

1. The USD is the currency of the United States.
2. Iran does not trade with the United States, not by its own choice, but because of a US embargo on all Iranian products.
3. Iran cannot trade in USD (from the US) because the US does not allow it.

Iran does not trade in USD because the country that the USD is backed by does not trade with Iran. This is the same reason that Cuba doesn't trade in USD.
The petrodollar theory does not apply because Iran has no choice in the matter. Even if Rouhani decides that he loves the US, he cannot trade in USD because the US has imposed an embargo. The Iranian propaganda department may claim that they are choosing to not trade in USD, but in reality it's not their decision.

If this embargo did not exist, I might agree with petrodollar theory. However, the embargo does exist, and so long as it does Iran cannot trade in USD regardless of what it wants to do.

I am not "disagree[ing] with facts and conclusions". The facts are that Iran is not trading with the USD because of the embargo. This is not a theory like petrodollar, this is the reality of the situation.

My opinion is this: Were the embargo to be lifted, would Iran trade in USD? More than likely yes. Cuba, which has had an embargo for much longer, and has been a much more serious enemy of the US, is still willing to trade if the US imposed embargo is lifted.