Saltimbocca is usually a veal escalope wrapped in Parma ham with sage. The ham and the sage are, however, just as complementary to red mullet.
While the Italians usually choose to eat their fish whole and on the bone, this is one l prefer to fillet because it has excessive quantities of small bones. If you did cook the fish whole, it would have to be unwrapped from the Parma ham before it could be eaten and your enjoyment of the dish would be impaired by the necessity of picking out small bones. The whole point anyway is to take a mouthful which incorporates all three elements - hence fillets are essential.
Red mullet is a very delicate fish to scale, gut and fillet, and fishmongers on the whole tend to be rather too violent with it It is also a very easy fish to dissect and therefore a good one to learn how to fillet on. This recipe, however, also works very well with fillets of brill or halibut.