In Association for Molecular Pathology v. Myriad Genetics, Inc., the Supreme Court ruled that synthetically created DNA is patentable, but the isolation of unaltered gene sequences is not.
AMA J Ethics. 2015;17(9):849-853. doi:
10.1001/journalofethics.2015.17.9.hlaw1-1509.
Publicizing physician ordering information as a way of peer-pressuring hospital employees into cutting costs is likely to have unintended consequences.
Even if they are not sick, people in quarantine are still patients; the physician is responsible for their well-being and may find that it is necessary to advocate for them.