Definitely not true at the present. A French archaeologist named de Cessac made a very nice early collection (1880s) which has some outstanding material, much of which is unavailable today, but excavations since that time have increased the quantity of Chumash material found, most of which is in local institutions. The Santa Barbara Museum of natural history houses a great deal of material, including the growing collection from Channel Islands National Park.

This later material at the museum has some notable material as well, such as the earliest human skeletal material from North America (Arlington Man from Santa Rosa Island). UCLA, UCSB, the University of Oregon, and the Los Angeles Museum of Natural history also house some really significant stuff. And more is coming in as research on the islands continues.

Juana Maria's cormorant skirt was presumably sent to the Vatican; if it ever was there, it is now lost. Her water bottle and some other artifacts went up in smoke in the 1906 San Francisco earthquake. Navy archaeologists have located the remains of her dwelling on San Nicolas.