ZV, if there is a core charge, and you request the part anyway, then you pay the core charge also.
I've never heard of a federal law regarding replaced auto parts. I think that is left up to the states. It may be, though. They do have to give you the old parts if you ask for them....after all, they are yours.
Edit: Taken from the Federal Trade Commission site:
"What do I need after the work is done?
Get a completed repair order describing the work done. It should list each repair, parts supplied, the cost of each part, labor charges, and the vehicle's odometer reading when you brought the vehicle in as well as when the repair order was completed. Ask for all replaced parts.
State law may require this."
Check with your A.G.