Primarily it's because 1) MP students still have 'MP' on their epaulettes, 2) much of their QL3 course MP students spend in OPDs (the police-style uniform) while driving in police vehicles (that also identify them as student MP vehicles, but still...) and 3) if they've had QL5 Reserve Qual prior to joining RegF they would be entitled to wear the red beret. In most QL3 courses there are a significant number of students who meet this criteria.
All of this leads to the possibility of members, or more likely civilians, to mistake MP students as badged MP members able to assist them in a law enforcement capacity. The CFMPA seeks to remove that liability as your average CFSEME student, for example, would not be called upon to do the things expected of a trained MP in an emergency, hence the extra precaution of identifying them as untrained.