The Skin Effect. The Skin Effect applies only to changing electric currents, including AC power transmission, radio signals, brief impulses, and even light. There is no skin effect for continuing currents, if you have DC, then the charge flows throughout the entire wire.
Skin effect depends on conductivity of the metal and on frequency of the current.
Lightning is an impulse current, so the Skin Effect usually does cause much of the current to be on the outer surface of a metal cage. The path for current will be through the metal car body. When a conductive object is given a DC charge imbalance, the imbalance appears only on a molecule-thick skin, and the electrostatic fields only appear outside the object. Faraday shielding during a lightning strike only prevents your body from taking on an imbalanced charge. Your hair would not stand up, and there would be no corona discharges off your fingertips.