The headlines are exaggerated. It is not a base, but a few buildings for training on a US military Base (Mountain Home in Idaho) as part of a foreign sales agreement for the F-15QA varient they purchased. Many other militaries have similar agreements and facilities, like Germany out of Holloman in New Mexico.

Still not a good look to be quid pro quoing with a fancy new Boeing and training centers, but it's far from "a foreign military base on US soil. Hell, even your standard foreign embassy in the US is more distinctly foreign than this facility.