Correct. These two Osage members did research and wrote a book that questionably places their tribe in the cave. However, the cave drawings were done by the Mississippian people that would be related to the Cahokias, or another group in the Southern Ceremonial Complex. If anyone has claim to the cave it would be the Illini confederacy who were enemies of the Osage, and the Illinis were probably not even descendents or diaspora of the Mississippians either.
There is nothing Osage about this cave. The Osage have even stated as such previously when they gained possession of Sugar Loaf Mound in STL. They said that they are the spiritual descendants of the mound builders but share no direct lineage. Same for the cave.
Their possession of Sugarloaf has left it gated for 11 years with almost no renovation done and no opening of a interpretive center. It should go to the Cahokia Mound Museum Society as an extention of the Cahokia Complex.
These two people are not speaking on behalf of the Osage but drumming up press for their book.
edit:sorry there is no lawsuit.