This is a DATABASE. Everything you do ingame is in it. It is queryable and they can build simple GUIs to execute those queries to search for user above normal usage.
Log files are different, and are more debug logs for identifying specific errors in the game. Log files are excessively verbose and when he said they don't keep logs, he was probably right. They get large fast. They may maintain simple logs such as this IP connected to us at this time, but not logs of every time your character takes a step or swings his weapon. They can enable those logs but only when troubleshooting a specific issue.
As far as items you pick up, time you've spent playing, experience gained, those can be seen through the database which is easy to query and retrieve that info. There is a timestamp when your character logged in and when he logged out, bam, there is something that is stored in their database and can be searched. etc.e tc.