After I went to bed I think I figured it out.
The power is coming from another box maybe an outlet.
Here is the "path" of the power.
In the power box the black power is connected to the black from the light.
The white from the light is connected to the white from the switch.
The black from the switch is connected to the white in the power box.
In other words as people have said the neutral is being switched.
The reason why he got voltage from the white at the switch was because he was completing the circuit. I guess the internal resistance in the multimeter kept the light from glowing brightly.
Easy enough to fix if you now where the power comes from.