You are missing or deliberately glossing over the important points. These are:
1) A speeding ticket is trivial. So why have your aide deny it existed?
2) The issue is, as I understand it, has she attempted to use channels that don't exist to Joe Bloggs to do whatever it was regarding the course - Graunaid:
"Under the proposal, Braverman would not have had to attend an in-person course with other motorists, or an online one where her name and face would be visible on camera to other participants.
Sources claimed that Home Office officials emailed the Cabinet Office’s propriety and ethics team to ask whether they could advise the home secretary. They were immediately told they could not.
When the civil servants refused to help, Braverman is believed to have turned to a political aide who tried to persuade the course provider to agree to the proposal. When they declined, she opted to take the three points on her licence and pay the fine instead."
I don't know whether this is a ministerial code breach, but the last bit in particular doesn't sound above board.
So why not have the investigation, find out what happened, and see if she breached the ministerial code?
It would be delicious to see her undone by the civil service blob.