I think you are confusing the Great Basin, a huge closed catchment, with the Basin and Range geologic province in which Yucca Mountain is located. The Great Basin is located in north central Wyoming, while the Basin and Range Province includes parts of several Western states including Nevada, where Yucca Mtn is located, and south central Oregon. 

Here's what happened to Yucca: "Site characterization work at Yucca Mountain indicated that projected radionuclide releases would exceed the EPA Radiation Protection Standard for geologic repositories within the 10,000 year regulatory period. DOE efforts to have EPA relax its standard failed.."  1992     https://www.nirs.org/wp-content/uploads/radwaste/yucca/yuccaroleofgeology115.pdf