FAC and CMC are different concepts. CMC will just record a value for accounting purposes and let the call go through while FAC will check for the autorization level. If you are using FAC and would like to know the actual code they press you should be looking at field authorizationCodeValue.
There's actually a service parameter in CallManager that determines if the value you input is recorded into the Flat file. It's called something like Display FAC in CDR. Make sure it's enabled in every CUCM server.
These are the paths to get to each CCX logs through CLI. They may be helpful if you are having issues accessing RTMT or downloading logs through it.
If you want to download them you have to prefix "file get " and you can add one of the options (re...