"It's important that those items sit in the dirt. Once it gets out of the dirt, if it's not recovered adequately, it's just a thing on the shelf. It has no importance to history. You've lost the entire story of what that piece meant, and you lose all ability to reconstruct the past, the settlement of the West and how people lived. These are generally not the people in history books; they're not wealthy. The only thing that remains is the archaeological record. If you take that out, the story is gone. All it does is sit on your shelf."
His phrase "recovered adequately" clearly means meticulously recorded and excavated by trained professionals in a forensic manner, with full regard for its context (the whole site, any related structural remains or features, stratigraphy, associated objects, and so on). That is the only way that the object can help to reveal the entire story of its past instead of ending up as just another meaningless bauble in someone's private home.
It all seems patently obvious to me but an American detectorist cannot understand: "I don’t know about you but I am damn tired of hearing this. It gets old real fast! ... Jeezus I just don’t get it." I gather he is 73. I'd hazard a guess that if the penny still hasn't dropped by now, there is a strong chance that it never will.
He appears to be under the weird impression that his treasure hunting is really some kind of frantic rescue operation, a sort of self-appointed one-man task force in a desperate race against time. Even though some of the artefacts have already sat quietly buried for at least over a hundred years, he seems to think that he is saving them from some imagined catastrophe about to strike any second - all for the public good of course, despite the fact that the artefacts will have now been forever robbed of any context that may have given them meaning and instead are likely to end up as just another piece of useless bric-a-brac in his private home. In addition, the sites where the artefacts were found will have now been devastated too - thoughtlessly stripped of evidence that may have helped to interpret them.
Curiously, the detectorist even objects to the use of the word "steal" by one archaeologist referring to private people taking things from public land. He says the use of the word is "totally uncalled for and just wrong. Do detectorists sell their relics or historical finds?" I appreciate that the detectorist is no longer in the first flush of youth but unless definitions have changed dramatically over his lifetime, I suspect that someone going into a public park and taking the benches, lamp posts or flowers has always been known as a thief, regardless of whether they sell them or not.
The British Museum is also public property. That doesn't mean a single member of the public can go inside and simply help themselves to anything they want. Most things described as "public" belong to the public as a whole entity, not to individual members of it.
(Clue: discovering history relies on context, NOT just objects.)