If you listened to the not too terrible Do you lose the right to privacy after you die? episode, then you are one step ahead of everyone else who reads this post, as you are already familiar with Malin Masterton. I cited her PhD thesis on repatriating remains held in museum collections. Masterton's position is based on the idea that, since a person leaves a legacy in the form of his or her identity, which is built during life and survives the individual after death, one can indeed injure a dead person by injuring the identity. This protection of dignity, contests Masterton, should be extended to the individual's remains as well.
The idea that the dead can be injured and should enjoy similar legal protection as the living is one root extending from a growing tree of thought that includes the view of archaeology (especially in the 19th and 20th centuries) as little more than academia-backed grave robbing. This is not to be confused with the period where medical school academics paid grave robbers to deliver fresh corpses for dissection. Archaeology's past is, however, in the eyes of some, equally morally reprehensible, especially in the frequent and common cases where well-heeled Western schools and institutions colluded with a nation's seat of power to remove the common cultural heritage that belonged to all people in a nation or, even more specifically, to a particular ethnic group that the seat of power was supposed to represent or at least look out for when dealing with Western museums.
There is a response, perhaps a survival response, among the fields that fall under the umbrella of anthropology and among archaeology in particular. In 2011, Yale, for example, famously gave back 366 of the 4,000 artifacts (including human remains) looted from the sacred Inca site, Machu Picchu, in Peru. This was 100 years after it accepted the items from archaeologist Hiram Bingham. And if you listened to the SYSK episode on shrunken heads, you would know that the Smithsonian's National Museum of the American Indian repatriated tsantsas to the Shuar beginning in 1999. (And if you're the best kind of SYSK listener around you will know that the concept of repatriation first came up in the Totem Poles episode and that we mention in the U.S. Marshals episode that the Marshals "arrested" a shipwreck off the coast of Rhode Island to protect if from looters.)
The idea that sites of historical and archaeological significance should be documented and preserved rather than looted (including a special emphasis on human remains) is creeping across the land and spilling into the sea to also include shipwrecks and underwater archaeological sites in general. The BBC has a great article on this, including an interactive map that highlights some protected and controversial underwater sites. Viewing the sites of maritime disasters as de facto marine burial grounds isn't entirely new. The discoverer of the Titanic, Robert Ballard, treated the site as a graveyard and reverentially refused to remove any artifacts. The decision was made to leave the remains of the crew members who went down on the U.S.S. Arizona at Pearl Harbor, and the site is now a protected graveyard. Japan similarly designated Truk Lagoon a cemetery, which is thus protected.
It's relatively easy to extend this protection to fairly modern shipwrecks, since you could still possibly run into the bones of the sailors and passengers when pillaging the site. But what about wrecks that are so old the bones (and thus the terror and guilt) aren't around anymore? Should they enjoy protection still? What if they also have really, really valuable artifacts aboard them?
I suppose the answers to these questions are best answered by other questions. Does a grave lose its command for reverence once the bones become clay? Does a people lose protection of their sites when their civilization is long collapsed? Answering these questions could not only further the field of archaeology, it could also provide the blueprint by which cultures respectfully interact with one another.