Please define "crop," and explain how that differs from "trim." In my world, it doesn't … The printer trims (physically "crops") the printed piece at the designated trim marks.
When you say, "TrimBox is set to 0.125 in since we gave this file 1/8" bleed," you lose me. The printer does not trim at the bleed marks. The customary .125 bleed is only an allowance in case the printer doesn't hit the trim marks right on the nailhead. The trim marks indicate the desired edges of the final printed piece.