Where is it defined in any of the acts that insurance is only waived on your own private property? Although private/leased property would be a fine example, it is not exclusive. As per the Compulsory Automobile Insurance Act:
2. (1) Subject to the regulations, no owner or lessee of a motor vehicle shall,
(a) operate the motor vehicle; or
(b) cause or permit the motor vehicle to be operated,
on a highway unless the motor vehicle is insured under a contract of automobile insurance. 1994, c. 11, s. 383; 1996, c. 21, s. 50 (3).
Definition of highway as per the Highway Traffic Act:
“highway” includes a common and public highway, street, avenue, parkway, driveway, square, place, bridge, viaduct or trestle, any part of which is intended for or used by the general public for the passage of vehicles and includes the area between the lateral property lines thereof; (“voie publique”).
There is no specific requirement in that definition that the private property or area must be owned or leased by the same person who is operating the motor vehicle. No need to extend the definition beyond what is already clearly stated in the acts. If I had a friend or family member with a large property and had built a trail, I could operate my motor vehicle on it with his consent without the need for liability insurance as this private trail does not fall under the definition of "highway". If the owner was prudent enough, he/she would make me sign a legal waiver absolving him of any responsibility for my injuries.
We must also be careful with thinking that just because an area is privately owned that this automatically waives the need for compulsory auto insurance. A parking lot is a good example. If I own a piece of land and I decide to build a store and a parking lot for customers where they can freely enter and leave, even though I own this lot, because it is used by the general public I cannot operate my motor vehicle on it without insurance. This is why the acts are not defined based on who owns the property but based on whether you are operating your vehicle in a public space.
Also per the Highway Traffic Act;
“motor vehicle” includes an automobile, a motorcycle, a motor-assisted bicycle unless otherwise indicated in this Act, and any other vehicle propelled or driven otherwise than by muscular power, but does not include a street car or other motor vehicle running only upon rails, a power-assisted bicycle, a motorized snow vehicle, a traction engine, a farm tractor, a self-propelled implement of husbandry or a road-building machine; (“véhicule automobile”)
“motorcycle” means a self-propelled vehicle having a seat or saddle for the use of the driver and designed to travel on not more than three wheels in contact with the ground, and includes a motor scooter, but does not include a motor assisted bicycle; (“motocyclette”)