Generally speaking, the transmission is lubricated by the pump, which is driven by the input shaft to the transmission. If the engine isn't running, this is generally the problem. (Manual transmissions don't suffer the same issue because they are generally splash-lubricated). *some* vehicles can be towed for short distances at limited speeds without incurring any damage, which is why tow truck drivers can often get away with doing so.
Now, it's entirely possible that the Mazda engineers who designed the transmission have provided a different means of lubricating the internls with the engine off. I've heard of some transmissions whose tail bearings are splash-lubed, and it's entirely possible yours is one of them. I'd certainly put my faith in the engineers that designed the system over a tow truck driver any day!
