One of the difficulties with this provision, and you are perfectly right, is that presently the Commissioner conducts an investigation “if he or she has reasons to believe”. So this is already a test of some sort.
If he receives a complaint, he must have “reasons to believe” that an investigation is necessary. This test would not apply when a parliamentarian requests an investigation. Therefore, once the Commissioner receives such a complaint, he would not investigate because of any “reason to believe”, but because a parliamentarian brings in a request to investigate. Do you understand? It looks like a double standard. It is a matter of fairness as to the Commissioner's approach.