Most people who see the Aleppo Codex see it at the Shrine of the Book in the Israel Museum in Jerusalem, in the same building as the Dead Sea Scrolls, and reasonably assume the museum owns it. It does not. What remained of the codex was entrusted in 1958 to Israel's second president, Yitzhak Ben-Zvi, and to the institute he founded, and it is a board of trustees under that institute, and not the museum, that holds it. A loan agreement signed in 1986 is why it is on the museum's wall.
The split is worth understanding because it is common and almost never visible to a visitor. The body that owns an object decides what may be done to it, who may examine it and what may be published from it. The body that displays it decides what a visitor sees and reads. Where those are the same institution a reader cannot tell the two roles apart, and where they are not, as here, a question about access goes to one address and a question about a label goes to another.
The institute has also published the codex in full online, image by image. For a manuscript this fragile that is a more consequential act of custody than the display is, because it removes most of the reasons anyone would need to handle the object at all. The atlas records the institute as the custodian and the museum as the place of display, and keeps the two facts apart deliberately.