If you showed up and worked, and were allowed to do so, then you MUST be paid for the hours you worked, regardless of whether the company had already said they had fired you or not or wrote a letter saying your last day was one thing when it was actually another. I have heard this one emphasized by DOL Wage and Hour officials enough. If you don't want this person paid, do not allow them to work. If you condone their presence at your place of business by allowing them to be there and to work, you will end up having to pay them.
What I am reading from this is that the person messed up something at their work when they "in-passed the secret shopper" which led to a termination letter which says they were discharged "for violation of a company policy.' They received this letter and it says they were terminated on the 21st, when they had actually already worked on the 22nd and the 23rd. They have not been paid for the work done on the last two days. They disagree with both the letter of termination's date of last work and their reason for termination.
It doesn't really matter about the reason they've put down on the termination letter. Go on and file for unemployment insurance and tell them what YOU believe to be the reason you were terminated. Tell them the date you last worked according to YOU. They'll sort through what actually happened.
Call the federal Wage and Hour division (1-866-487-9243) if you are not paid for those last two days you worked. These two things, unemployment and the wage and hour department are the only recourse you have as far as any kind of case.