Sounds like they want you to replace the Body Control Module. Since the A/C compressor does come on if one of the two lower blower settings is selected, I'd be inclined to think that the BCM is working fine and that the HVAC control module is not sending an A/C r
equest signal when the blower is set to one of the two higher speeds. Of course this is assuming that everything else is in working order and all conditions are met to allow the compressor to be engaged.
If I were a betting man without knowing anything else, my money would be on a bad HVAC control module, not a bad BCM. Usually BCMs fail in a catastrophic manner that affects the functionality of many circuits, not just one.
EDIT: Sure enough, GM issued TSB #04-01-38-006
for this issue which says to replace the blower motor resistor or the HVAC control module if resistor tests fine.