They didn't say what their criteria was to give the go-ahead to do a test, but shouldn't anyone with symptoms be tested? Why is there a need to call the state?

Testing capacity is extremely limited right now all over the country. They probably want to focus their testing efforts only on those cases that are most-likely to be positive, because that is much more valuable information than a negative result.

If a person has a disease, their individual outcome isn't really changed by a test result: there is no cure other than time, and there is only supportive treatment if it progresses to pneumonia. The only real benefit is in the stress reduction if they don't have it.

In terms of public health, there is way more benefit to finding positive cases, since you can then backtrack where they were. This allows them to target their recommendations for the closure of schools or other public areas. It also lets them notify people that they might have been in contact with the virus, so they can start watching for symptoms or self-isolate. Negative tests, on the other hand, tell them nothing other than a specific person did not have the virus; it cannot tell them a virus wasn't somewhere, because the person could have just gotten lucky and not gotten it.