I think your inspector is correct. You are penetrating a rated floor assembly (which also probably doesn't meet the IIC requirements). The penetration needs to be firestopped. In commercial construction they "prerock" the areas where there are penetrations during rough-in. Install enough gyp to make all your penetrations and firestop, then when you rock the rest of the room, you butt up to the prerocked area and tape the joint.I will have to completely disconnect the plumbing and figure out how to run it through sheetrock.
Approved plans form the city are no defense against code violations found later during construction. Also, firestopping is rarely submitted for permit. The contractor is responsible for getting all the penetration firestop designed and providing the inspector with the listed systems at the field inspection.
This inspector sounds like he's just doing his job.