"...you cannot hunt big game in Southern Ontario with a centerfire rifle..." Nonsense. Everything South of the French River is considered to be Southern Ontario. Depends entirely on the WMU.
The Ontario MNR has decided shotguns can have 3 rounds only in the firearm. Get caught with 5 and you'll be charged under the Fish and Wildlife Conservation Act. Plus lose your shotgun, your hunting licence and the CO can confiscate everything you have with you, including your vehicle.
"...isn't it a 12 gauge _rifle_ ?..." Yes, but a shotgun with a rifled barrel is still considered to be a shotgun in 'shotguns only' areas. Asked the MNR a few years back. Logic, of course, has nothing to do with it.