Isn't a vapor barrior to protect the insulation from moisture? I think without it, mold will occur. Not sure what your garage door has to do with that.
I'd say yes and no. It is there to prevent moisture from migrating through the wall and condensing at the point within the wall where the dew point is reached. This is necessary in a house because cooking, bathing and just living (i.e. breathiong) produce moisture which builds up producing vapor pressure. The moisture will migrate wherever it can to get to the drier outside air. This is controlled through sealing areas where moisture shouldn't go (i.e. wall cavities) and providing venting (usually mechanical) such as vent fans or even air-to-air heat exchangers.
In the garage he probably isn't producing that much moisture. In addition, because the door is large and not well sealed he is probably getting a lot of air exchange just around the door. The garage is also probably not kept at as high a temperature as the house so the garage air won't hold as much moisture (warm air will hold more moisture than cooler air).
So, it may not be problem for him not to have a vapor barrier in the garage depending upon what he does out there, how warm he keeps it and how much air exchange he's getting around his door and other places (often garages have holes designed in a wall for combustion air for a furnace, water heater or other fuel burning appliance).
All that said, normally these days garages are built with a vapor barrier just like the house as a precaution against moisture condensing in the walls or ceiling.