This absurdity that the government "owns" "historical" (and they often use a very broad definition of "historical") found on your property has done much more harm than good, especially in Europe.
What this is saying to those who might find historical artifacts is to either ignore them or avoid recording them. This is counter-productive to the preservation of history. Instead, what needs to happen is we need to let the market help history. For example, a dug arrowhead is unlikely to fetch much money at market, but a dug arrowhead with a story behind it will often fetch much more, thus giving an incentive to have finds "checked out" because that means extra $$$ for you when you sell it.
Of course it also has a more outrageous claim, the claim to own things on your own property. Whatever is buried on your land, be it an Anglo-Saxon hoard, oil, or whatever is yours to do with as you wish so long as you own the land.