I would guess that the anecdote about the woman who can't get tested is because of a severe under supply of test kits. The CDC developed a test kit last month, but it is only being sent to approved laboratories, and the tests will only be given to people "who meet CDC criteria for COVID-19 testing." [1]

Test suppliers who develop test for hospitals and doctors offices are ramping up production as fast as they can, but it will take time.

[1] https://www.cdc.gov/coronavirus/2019-ncov/about/testing.html