My house is currently under construction. I had an independent inspector come out and he said that the bathtubs should be secured with clips that come with the tubs that attach to the side of the bathtub and are then nailed to the studs. The builder says that the tubs are secured by the drywall and he's never heard of clipping the tubs to the studs. Which is correct?

If the clips come with the tub, by all means they need to be installed. They are common on fiberglass and acrylic tubs. A steel tub is secured by a stringer. A stringer, or ledger (as some refer) is a 2x4 that the back edge (opposite the apron) rests upon. Don't alway's rely on just what the builder tells you. If you have any specific questions, go right to the source (plumber, electrician, carpenter, etc.) They will be more than happy to answer your questions.