this article from the same site seems to say otherwise:


On the legal side, the EUA statute says nothing directed at employers or universities. Instead, it addresses the actions of federal officials, such as the HHS secretary and the president — not private actors. Private employees are generally “at will,” meaning they can be terminated for any reason that is not explicitly illegal. Those arguing that the EUA statute prohibits mandates by at-will employers are claiming that this federal law is changing existing state employment law on the topic by mere implication. They are reading in a broad prohibition covering all employers and universities in the U.S. that is not, in fact, in the statute. Such broad preemption would require, at a minimum, clearer language.


During the pandemic, employers and universities have already required Covid-19 tests, many of which are being provided under emergency use authorization, for their in-person employees and returning students. If mandating products like tests under an EUA is unlawful, then every employer or university requiring the use of those tests has been flagrantly violating the law.

Before the pandemic, the general position of the relevant federal agencies, such as the Food and Drug Administration and the Centers for Disease Control and Prevention, was that vaccines provided under emergency use authorization cannot be mandated. But that guidance was not binding. When confronted with pandemic realities, the federal government took the position that “[w]hether an employer may require or mandate Covid-19 vaccination is a matter of state or other applicable law.” Legally, there is nothing to prevent such a reasonable position shift.


[link to www.statnews.com (secure)]