Last December, my mother flew in business class to Manila from Detroit. Guess what? All the business class pax were the last ones to receive their bags in MNL!
When I flew to MNL a few days later, 3 out of 4 bags came out within a few minutes of the carousel running. I got impatient with my last bag, and I asked a baggage handler if its coming. After mentioning that I was first class, he immediately radioed someone inside the aircraft to find it and immediately place it on the carousel.
"First/business class" is the magic word to getting service.
From previous experiences, int'l first/business class pax in DTW get their bags pretty quickly.