The Graph indicates a very high positivity rate in March/April that dropped and has ticked back up.
But consider that in March, April and May you were only testing people who were had symptoms, as the testing infrastructure wasn't well established. So the positivity rate was much higher. In New York and California, you saw a positivity rate around 50% in April.
Now that people can get testing for screening purposes and there are places like New York where positivity rate is now around 1%. Those are things that would naturally drop the National positivity rate.
But in states that are struggling, the positivity rate is still quite high considering how many people they're testing.
Florida: 19%
Texas: 15%
Arizona: 24%
Georgia: 15%
This indicates that they're testing a lot of sick people. And we've all seen lineups at testing facilities. https://www.usatoday.com/story/news/health/2020/07/11/covid-19-test-results-delayed-labs-struggle-cases-surge/5406936002/
I doubt people would endure that unless they really thought they had the disease.