I haven't really followed this, but I'm guessing the 'rich people's one to one' course was also a way of trying to keep the whole thing secret? Plus, the idea that she got (or tried to get) departmental officials to sort this for her - ordering your work subordinates to sort out a private criminal justice issue - all of that should certainly mean she should go. And when you factor in she's a loathsome scumbag...
She was fucking stupid to ask for it yes. I can objectively understand why in terms of people recording it, but the optics are terrible. I'd go the opposite way and publicise it, pointing out the dangers of speeding, hold her hands up. Make political capital. Not try to cover it up.