Sternberg is not an employee of the Smithsonian. He's an employee of NCBI.
I don't think it is going to matter what his affiliation was concerning the Smithsonian. It is an abuse of power for one on the public dole to try to destroy a person's career, reputation and such:
I'm sure they'll find several legal theories to pursue - discrimination, abuse of power, tortious conduct and who knows what else... Once it is in court, the Smithsonian cannot refuse to cooperate.