She got on the plane because she had a valid Iranian passport, but to use that she had to pay for a visa to enter the UAE. Her original objection appears to be that she didn't want to pay for a visa and that is why she got stroppy. From then on it was never going to end well. There are also some reports that she was providing Botox services in the UAE for which she wasn't licenced so it is possible she actually got off quite lightly.
For sure, this story had nothing to do with alcohol consumption and everything to do with bad journalisim.