I don't think any such discussion now is going to matter very much. I think the fact that you claimed to not have the means to pay (whether genuine or false) would have been noted so this would have gone down the usual route of how such matters are dealt with. Being able to prove that you actually did have the funds is not going to play to your favour, because you either had no funds on the day, or you lied. This is how it will be viewed.
I agree that you probably acted irrationally at the time, but you may as well now go along with it, or you may find yourself in deeper trouble. Opportunist fare evasion mostly results in last-minute decisions. They are quite common and do not always have an explanation.