Nay.
I know that’s the official position, but it’s just not true.
There are sick people with known exposure in home quarantine that still cannot get tested.
https://techcrunch.com/2020/03/08/u-s-response-to-the-covid-19-coronavirus-moves-from-containment-to-mitigation/
You are correct as of this moment—but that is expected to change in the near future.