When you checked the wire, was it still connected at both ends? Or did you disconnect it and measure between your end of the wire and the housing?
If you are measuring and finding a ground between wherever and the housing, you need to remove the bulb first. If the bulb is in place you will see the circuit as a ground because it's finding it's ground connection through the bulb itself.
Remember that when using a volt/ohm meter, ALL circuits will show a ground if they are complete.
Only by turning a switch off, or by removing the load (in this case the bulb) will give an accurate reading with an ohm-meter. It's too sensitive otherwise, and will detect even the barest minimum of grounding connections. In this case through the case of the bulb, to the socket, to the housing, and to the body.
Paul