I think it may be more accurate to say a tractor "can push NO MORE than its own weight..."
This is assuming perfect traction. On dirt or turf, you are going to be about 1/2 of that.
Add any incline, and the maximum drawbar force starts to come into play (max torque in lowest gear).
Add loose dirt, snow, or worst case, loose sand, and you are going to use up tractive force and torque just moving on the soft surface. Rolling a wheel through loose sand, for example, can be similar going up to a 20 to 30% grade!
I do aree with the partial lifting concept, though. Even of the loader can't lift the object at all, by having a constant lifting force, you are transferring weight from the object to the tractor's wheels.
- Rick