I can offer a somewhat different perspective. I had a friend who was lucky enough to discover several rare and valuable mineral deposits in New England. The Smithsonian traded him fine mineral specimens from their collections in exchange for the opportunity to obtain nice specimens from him. And, in the world of meteorite collecting, museum trades are the norm, not the exception. Museums depend on meteorite hunters/ collectors to obtain specimens of new falls and finds of meteorites. Museum curators will gladly exchange rare and valuable meteorites to a collector in exchange for what the collector/hunter may have to offer. It's a very common practice and private collectors are able to obtain specimens missing from their own collections through such exchanges from museums. Certainly, at least where mineral and meteorite hunting is concerned, museums fully support private collectors, and especially where meteorites are concerned, museums count on collectors. As do meteorite scientists as well. There is a symbiotic relationship among collectors and scientists in the world of meteorites.
In the case of my mineral hunting friend, he came to know the mineral (and fossil) curating personnel at the Smithsonian, and they certainly came to know him. Everything on a first name basis, and never any discouragement that he should not be hunting and collecting minerals.
i am aware that it is likely a far different story where cultural resources are concerned. Museums have been forced to return portions of their cultural collections to the tribes, for instance. But, at least in the world of mineral and meteorite collecting, museums get along just fine with collectors, and depend on collectors to grow their own institutional collections.