Adventure! Suspense! Excitement! You've come to the wrong place for these things.
Semantics! Pedantry! Ambiguity! That's more like it.
This is an essay (partly) about the American Museum of Natural History's Central Asiatic Expeditions of 1922, 1925, and 1928, and those expeditions certainly had their share of adventure, suspense, and excitement. The expeditions' leader, Roy Chapman Andrews, gathered fame and acclaim when he returned from Mongolia with tales about gunfights with bandits and contact with unfamiliar cultures (1932) . He also returned with a wealth of fossil material, including newly-discovered dinosaurs--even the first known dinosaur eggs --and extinct mammals. The proper ownership of the expeditions' fossil finds have since become a matter of some controversy. This essay is also (and mostly) about that last part.
In 2015, a Mongolian envoy visited the AMNH to discuss repatriation of the museum's Mongolian fossil material. Shortly thereafter Bolortsetseg Minjin, the president of the Institute for the Study of Mongolian Dinosaurs, issued this statement, which has recently been making the rounds on Twitter . Minjin argued that repatriation from the AMNH at this point would be impractical given that the Mongolian fossils 'are so central to their institutional identity.' And so here we come to face the central moral question of paleontology: who owns fossils?
Philosophy includes three main disciplinary branches: metaphysics, epistemology, and ethics. Philosophers tend to fall into one of two camps: those who say that metaphysics is fundamental and those who say that epistemology is fundamental. One point to take away here is that ethics isn't even in the running for the coveted "Most Fundamental Subject" award. Another is that a properly philosophical way of answering a moral question, depending on what kind of philosopher you are, is to rephrase the moral question as one about metaphysics or as one about epistemology.
(Example: you ask, "is it wrong to steal a loaf of bread to feed your starving family?" One philosopher will respond, "what characteristic of the bread really make it someone else's property?" Another will respond, "how do you know that your family is going to starve?" One of the philosophers is probably hoarding bread anyway, given that philosophers are disproportionately vegetarian.)
We can say this much about the fossil ownership question: Andrews' approach to the ownership question puts him in the metaphysics-is-fundamental camp. In his own account of the Central Asiatic Expeditions, he described his negotiations for further expeditions: 'I was able to conclude an agreement...whereby we could go to Mongolia in 1930. But since they stipulated that all mammals, birds, reptiles, and archaeological specimens which we collected must be given to them, I decided to do no work except in palaeontology, geology, and topography' (1932, 421). Andrews clearly didn't think that fossil mammals, fossil birds, or fossil reptiles qualified as mammals, birds, or reptiles, or at least figured that there was enough of a semantical difference between "fossil mammal" and "mammal" to satisfy the terms of his agreement with foreign authorities.
I can sympathize (and have sympathized) with Andrews' thinking. In fact, the moral issue calls attention to a variety of other metaphysical distinctions to be drawn between organisms and fossils. There are good reasons for sovereign nations to protect their indigenous organisms: those organisms are interwoven in complex ecological relations that underwrite the nation's environmental and (consequently) economic health. Fossils don't have that particular kind of material importance. Fossils might take on cultural rather than ecological significance--Mongolia's "fighting dinosaurs" fossil has been declared a national treasure, allowed out of the country only once since its discovery in 1971 --but in this sense fossils might be more like human artifacts than (strictly) biological phenomena, imbued with meaning uniquely constructed by members of some specific group. You can give an answer to the "who owns fossils?" question, but whatever justification you give for that answer has to be very different from the answer you give to the (poorly phrased) question, "who owns organisms?"
And even if you aren't moved by Andrews' legalism or similar concerns, you can't avoid metaphysics in the debate over fossil ownership. To wit: what is the American Museum's "institutional identity"? Andrews agreed to provide the Mongolian government with 'certain duplicates of our collections' (Ibid, 272). It seems unlikely that the American Museum would be a substantively different institution if its Mongolian fossils were exchanged with Andrews' duplicates. (For those more inclined to put epistemology first: it seems even less likely that the Museum's visitors would ever notice the change.) Or: whatever identifies the American Museum, that identity was constructed through the intentional action of relatively few people. By contrast, the cultural identity of Mongolia was constructed through the collective--and arguably unintentional--action of many more individuals. One was constructed for fossils and the other (probably) wasn't.
My students often lament how moral reasoning leads "in a circle," meaning (I presume) that one can find objections to a moral question's answer and then object with equal aplomb to the suggested resolution. So it seems to go when viewed from the outside. Commit to a metaphysical view, though, and the road may have a beginning and an end, however curvy the space between might be. Andrews committed to a view of fossils as geological phenomena rather than biological ones and that commitment implied his answer to the ownership question.
 Andrews was a larger-than-life figure whose exploits bear some (perhaps-not-coincidental) resemblance to those of Indiana Jones (hence the first part of this post's title).
 Among the eggs discovered were some belonging to Protoceratops andrewsi--so named in honor of Mr. Andrews--a dinosaur whose remains might have prompted the myth of the griffon (hence the second part of this post's title).
 You are following us on Twitter, yes?
 Here's my favorite Roy Chapman Andrews story:
[American Museum of Natural History director of invertebrate zoology Herman Bumpus] listened indulgently as Andrews pleaded his case for a job. Nevertheless, all hope appeared to vanish when the director [insisted] that no suitable positions were available. ... Almost unthinkingly, [Andrews] blurted out that he was not asking for a position; he simply wanted to work at the Museum in any capacity, even if he did nothing more than clean floors. Bumpus protested that a man with a college degree would never be happy scrubbing floors. ... Andrews countered that he would certainly not scrub just any floors, but the Museum's floors, he insisted, were different. Unable to resist this outburst of youthful ardor, Bumpus relented. He agreed to hire Andrews as an assistant in the taxidermy department at $40 a month. (Gallenkamp 2002, 12)
If anyone from the American Museum is reading: not only do I love the museum's floors; I'm ga-ga for its walls and ceilings as well.
 Ironically enough, that one time was for a special exhibition at the American Museum of Natural History in 2002. It was one of only two museum exhibits that have ever moved me to tears. The second was Michelangelo's "Pieta." I've got a thing for organism-shaped rocks.
- Andrews, R.C. (1932). The New Conquest of Central Asia: A Narrative of the Explorations of the Central Asiatic Expeditions in Mongolia and China, 1921-1930. New York, NY: American Museum of Natural History.
- Gallenkamp, C. (2002). Dragon Hunter: Roy Chapman Andrews and the Central Asiatic Expeditions. New York, NY: Penguin Books.