Apparently the CID checks out PPLs also. I was interested a while back about PPL’s getting airside access without background checks, I spoke to the owner of the flight school I fly from, he suggested that the police ‘request’ (read: require) a list of pilots at the club. I am sorry I can’t help you with your question, however it would seem illogical if a caution prohibits you from a CPL, unless perhaps it was drug related.