Great illustration. The 4.8 million previous jobs brought back is a net number and it is understated. 588,000 old jobs were lost so the previous jobs brought back were actually 5.4 million. Nearly all of those are now at risk of a new layoff with the surging coronavirus outbreak currently going on as places now closing back down.
The other thing is the "mischaracterization" error still exists where people not working are counted as employed because their status is temporary layoff. Because they are not being paid they are supposed to be counted as unemployed. The footnote estimated that if they were correctly counted the unemployment rate for June would be 1% higher, or 12.1%. This error has been ongoing for the last 4 months now and it is hard to understand why it is so hard to fix. Some percent of these previous jobs filled and counted as new jobs this month were previously counted as employed because of the mischaracterization. No, they are not counted twice as being in the work force because there are two different surveys but it does present a rosy picture of the job situation - just as calling these new jobs does. Next month reality will set in again.