Jeff you are correct, the artifacts always belong to the property owner. As a contract archaeologist I am always asked that question. The property owner can donate the artifacts and many, many do for tax write-offs. You might have noticed in one of the episodes pin flags sticking out of one of the mens pockets. We use those to mark each target then sight each artifact in using a transit. That gives us a horizontal distribution of metal artifacts. With that knowledge we can then locate the historic features associated with the archaeological site. The archaeologists on the show, you bet, are overseeing the metal detector survey. Especially on sites controlled/protected by the national historic registry. I would imagine a lot of archaeologists do not approve of some aspects of the show. However, the show does promote recording finds and asking for permission as well as giving the artifacts to the site owners "museum" rather than selling them on E-bay. I also agree with your statement about potential values. One must remember that the most valuable thing to an archaeologist is understanding the life of the earlier time and recording that life for all to benefit from.
Hunting Success "Nature will teach you but you must spend time in her classroom"