Dr. Fauci is NOT the leader for infectious disease in the USA. That is false. His work on HIV/AIDS leaves a lot to be desired.
My better half works for the government, and is involved with the COVID19 outbreak, and she would agree with Dr. Fauci that 22% does not constitute herd immunity. Sadly, too many of these government bureaucrats are extremely literal, and not logical.
However, even with 22% of the population having immunity, that would reduce the spread of a disease. So I think it is fair to say there is partial herd immunity there. I suspect Dr. Rand Paul was implying that as a factor, nothing more.