The joint investigation by the Correctional Service of Canada and the Parole Board Canada is a mandatory, legislated investigation when tragic violent events such as this one occur.
The problem with these types of investigations is public perception. They give the impression that they are completely internal investigations, that they are only about investigating the organization. I would welcome an external investigation as well, if only to reassure the public and to show that the investigation is being done independently.
I'm not criticizing the work that was done, I'm criticizing the perception it gives.