Steven Litt's text on another US museum's dispute with Turkey over dugup items in its collection begins by discussing a bronze statue:
A large, headless, Roman-era bronze statue believed to represent Marcus Aurelius has reigned for 26 years as the resident philosopher-king of the Cleveland Museum of Art. With its lifelike presence, fluid drapery folds and dark, luscious patina, the sculpture is one of the museum’s signature treasures. Yet a mystery has always hovered over this exceedingly rare object. Where, exactly, did it come out of the ground, and who unearthed it? Just as important, how many hands did it pass through before it found its way into the collection in 1986? The museum has long stated that the work might have been found in the 1960s in an obscure village in southwestern Turkey called Bubon, but it isn’t sure. The government of Turkey, on the other hand, is sure. It says that the bronze and nearly two dozen other works in Cleveland were looted from its soil, although the country has produced no evidence. [...] former curators familiar with the Marcus Aurelius statue [...] say they don’t know where [it was] excavated before the museum bought [it]. Arielle Kozloff of Shaker Heights, the now-retired curator who led the purchase of the Marcus Aurelius bronze in 1986, traveled to Bubon later that year to investigate its origins. According to local gossip, villagers dug up the sculpture in the 1960s, along with many other bronzes, which appeared on the art market over the following two decades. But Kozloff concluded in a 1987 article in the museum’s bulletin that any connection between Bubon and the Marcus Aurelius was conjectural.The site at Bubon is accessibly summarised here. See also here. But there is more on this statue in David Gill's "Looting Matters" where we read a somewhat different story from that which Cleveland wants to promote ('Cleveland and Turkey: Marcus Aurelius and Bubon'):
In 1980 Cornelius C. Vermeule put together a list of Roman imperial statues that could be linked to the sebasteion in Bubon, Turkey. Subsequent to this in 1993 J. Inan published a list of some of the present locations, and this was discussed by C. Chippindale and D. Gill in 2000. [...] The year of acquisition, 1986, coincides with 5 pieces that Cleveland has now returned to Italy. 1986 is a date when due diligence does not appear to have been of paramount importance to the curatorial team in Cleveland. It is important that Cleveland reveals how it acquired the statue in order to show its commitment to the highest ethical standards.Despite the Cleveland museum saying it really does not know where the stature is from, Gill points out that "the association with Bubon is clearly stated on the Cleveland website".
There is a podcast here about the new display of the collections, the statue is mentioned at 2mins 10 seconds: http://www.wksu.org/news/story/25654
Vermeule, C. C. 1980. "The late Antonine and Severan Bronze Portaits from Southwest Asia Minor", in Eikones. Studien zum griechischen und römischen Bildnis. Hans Jucker zum sechzigsten Geburtstag gewidmet , Basel, pp. 185-190.
İnan, J. 1993. "Neue Forschungen zum Sebasteion von Bubon und seinen Statuen", in Akten des II. Internationalen Lykien-Symposions Vienna, 6.-12. Mai 1990, ed. J. Borcchardt, J. and G. Dobesch, Vienna 1993, pp. 213-239.
Chippindale, C. & D. Gill, 2000. Material consequences of contemporary Classical collecting. American Journal of Archaeology 104, 463–511.
Photo: "The Emperor as Philosopher, probably Marcus Aurelius (reigned AD 161�180), c. 175�200. Turkey, Bubon(?) (in Lycia), Roman, late second century. Bronze, hollow cast in several pieces and joined; 193 cm. Leonard C. Hanna Jr. Fund 1986.5"