Rock Pigeons (the common ones you see in the city) are classed as non-protected and a pest species - meaning that anyone can exterminate them. However the method used must be an approved method and it is still illegal to keep them in captivity without a special permit.

Also when a wild animal is contained, such as this case, then it does fall under the PCA act and the SPCA can and will respond.

The 2 numbers to call when you can get confirmation would be:
Canadian Wildlife Services 604 940 4690 or 1800 731 6373
Vancouver SPCA 604 879 7721

BOTH of those agencies can and should respond in this kind of case.