No it's not theirs to choose. There are strict rules. He can recommend the deaccessioning of an artwork or collection, but that just sets the motion. Guidelines from the Association of Art Museum Curators regarding deaccessioning are as follows:
The curator, or department chair, should initiate any recommendation for the disposition or deaccessioning of works of art from the collection. Procedures for approving proposed deaccessions differ from museum to museum: in many institutions, a curator’s recommendations are considered by the director and the appropriate committee and then submitted to a board of trustees for final decision. Curators must be candid and forthcoming with their director should they have any reservations about objects proposed for deaccession, whether or not the objects emanate from their department.
Strong reasons are needed for deaccessioning—for example, if the works are proven to be fake or misattributed, if the museum needs space that a large collection is taking, or if it is in financial trouble and needs money. Never will it happen simply according to the artistic taste of a curator. And since deaccessions are for selling the work, it would make a pretty bad sales pitch to say that the works are being "loaded off" for lack of artistic merit.
Moreover, there can be provisions in deals that prevents the selling of an artwork, part of a collection or the entire collection. Regarding Kenna, we don't know what the provisions are.