Justice should be transparent.
But when being offered an out-of-court disposal you are being given an opportunity to
avoid the justice system. Accepting that offer would see a very considerable discount compared to the cost of being dealt with in court - even if you plead guilty. The police see a considerable cost saving as well and that is why they will generally not engage in correspondence, because it negates their savings,
But to take advantage of that discount you must accept the allegation as it stands. If you don't want to do that then you can have the matter heard in court where all the usual rules of transparency apply. And of course, if you are right and no offence has been committed, you face no penalty.
By saying you are almost out of time, it gives me the impression that if you had been provided with the evidence that you seek and it seemed to show no offence had been committed, you would not have named yourself as the driver (or why else are you delaying doing so?). That would see you on the wrong end of six points, whether you were right or not.