I cannot say for sure on the X, but on the 3 Series this problem is usually caused by the level sensor. I checked the X5 parts diagram, and it does have this similar sensor. It is located in the bottom of the expansion tank. It can get fouled by coolant gunk and cause false triggers.
Click here, it's part #8 in the diagram. It should be the same for all X5 models in that year.
$4K??? Holy crap!!!
The first thing they should have done was to replace this $15 sensor and let you drive it a few days. Did they do that?
The second thing to do now is check the level first thing in the morning (i.e. when cold) VISUALLY UNDER THE HOOD. If you are at normal level each morning for a week, and still get sensor trips, it is NOT a coolant level/leak issue. And then you need to find a new service center!!!!!