HIPAA
The company cannot, by law, identify infected employees. They do have to work with health officials to identify people the infected may have contacted and those people should be quarantined.
The county health departments where these facilities are located would take care of this. When my daughter was quarantined, they contacted her boyfriend's employer to make sure that they understood that he was quarantined until a test came back.
County health officials take this very, very seriously and will put the fear into anyone that steps in their way.