The public health logic of the political donut shop

From the City of Atwater website:

Are there any reported cases in Merced County?

As of 3-13-20, there are no known reported cases in the County, so there is no cause for undue alarm. However, we still are taking all precautions to ensure plans and contingencies are in place to help protect the public, should they be necessary. – Atwater City Council, March 14, 2020;

But what if known cases have not been reported to a public agency required by law to report them to the public? What about known but unreported cases?

Does the public know a person has Covid-19 without a test?

Are physicians required by law to report patients' who test positive for the virus?

Can patients by law prohibit their physicians from reporting positive test results for Covid-19?