>The only thing I really see there though concerning polarity is the input which
>makes perfect sense, as that's DC. Not sure about the output yet though.
According to what I read on that site, the bare lamp operates on about 1000V AC. What you are calling the input is the input (power) to the DC to AC converter (inverter). The output is AC and so has no polarity. Since the bare bulb operates on AC, it has no polarity. There is nothing in the way it is made that would require one end to be grounded over the other.
Why does house AC have a polarized plug? AC in itself has no polarity. The purpose of the polarized plug is mainly to reduce the hazard of shock. House AC has one side of the power line connected to the earth, literally. Therefore if you accidently touch that side of the line and another part of your body is contact with the ground, the shock hazard is generally less because there should only be a low or zero voltage between the two. In addition the big round prong on the plug is directly connected to the earth and carries no current, unlike the "neutral" side of the power wire which does. Exposed parts in modem equipment are connected to the round ground prong. Therefore the most likely kind of electrical fault (faulty insulation) will likely only put that wire in contact with a grounded part and there will not be a shock hazard. The neutral wire, although grounded, carries current, and therefore developes a voltage above ground due to the resistance of the wire. In some instances the resistance, due to corroded or poor contacts, can be high enough to result in a hazard. Therefore a third prong, not carrying current was added to the original system.
In the older system (which is still in place), the neutral wire was connected to the electrical contact which was most likely to be touched. For instance in a light socket the outer ring, the part that contacts the light bulbs thread, is connected to the neutral. The center contact is the hot side, the side not connected to the earth. In order for this to make any sense, a two pronged plug has to have one wide prong, which is the neutral side.