When the bike is being trailered, the liability coverage for damage and injury caused by that trailer and trailered load falls on the towing vehicle. Same goes for a vehicle hooked up to a tow truck.
Take a different track. If you're pushing a disabled car down a wide sidewalk, are you not "operating" the car even though it is not running? If you have a collision and cause property damage or injury, how do you think the incident would be categorized? And why would a motorcycle be fundamentally any different?
If you've modified the motorcycle so that it is obviously no longer used as a motor vehicle, say you turned it into a baby carriage instead, then you could walk it down the sidewalk without impunity.
However, if its obvious use is still that of a motor vehicle (whether operational, insured, or not), at the very least you need to consider the motor vehicle insurance ramifications if someone's property is damaged or someone is injured while you're pushing that motorcycle down the sidewalk.