My training was always:
aerodrome message - METREPORT - magnetic (2 minutes average)
published METAR/TAF - true (10 minutes average)
ATIS should be METREPORT, but local installations say "... metar at 1300Z ..." which is different, but at least you know it. I tried to look in Annex 3 that such practice is incorrect, but didn't found any evidence.
FD (the un-real)