RasNas

Hello my family is applying for permanent residency for Australia and all was well until a couple of days ago where I was caught with possession of a marijuana... I asked the police officer if this could be traced by Australia and they assured me that it couldn't and was the lowest possible thing they could give me, like a street warning or street caution, all I had to do was sign a paper and I was free to go. They said it would be on the system for police officers only and if I was caught re offending then it would be a criminal record. Were they lying? (Which I don't doubt because I was tripping on LSD at the time and they may have not wanted to give me a really bad trip) One more ore question, does it matter if THC is found in the body when going for a medical? Or do they not even bother checking for it? Thanks!