The X5 uses the fog lamp also as a "turning lamp," to light-up the corner while turning. I suspect you are are simply seeing a side effect of this.

Driving Direction Condition Side with Activated Turn-Off Light:

Forward
•Speed below 40 km/h
•Direction indicator activated
Same side as activated direction indicator

Forward
•Speed below 40 km/h
•Direction indicator activated
On side in direction of steering lock

Reverse
•Speed below 40 km/h
•Reverse gear activated
•Direction indicator activated
Same side as activated direction indicator

Reverse
•Speed below 40 km/h
•Reverse gear activated
•Steering lock
Opposite side in direction of steering lock

Reverse
•Vehicle speed below 65 km/h
•Reverse gear activated
Both Sides