WeatherTalk: Lightning is just a huge spark
Inside a car is usually safe from lightning, but not because of the tires.
Lightning is a spark connecting regions of opposite charge. The charge separation often becomes greater during convective storms due to static charge buildup. Lightning often strikes tall objects such as trees or towers, but the current travels through the ground all around these objects, making it unsafe to even be in the vicinity of these things. Water and many metals are good conductors and so should be avoided.
A surprisingly dangerous place to be is lying on your back under a car in your garage. If the garage is struck, rebar in the floor is a good conductor. Inside the home, avoid handling things that are plugged in as the wires may carry current if the house is struck. A car offers a good measure of protection and is relatively safe in a lightning storm. This actually has nothing to do with insulating materials in the tires. Rather, lightning current is more likely to pass around the shell of the car than the inside.