Really? I'm not sure that's correct unless CDC opinion has changed since 23 May when they said*: "these observations suggest that the presence of antibodies may decrease a person’s infectiousness and offer some level of protection from reinfection. However, definitive data are lacking, and it remains uncertain whether individuals with antibodies (neutralizing or total) are protected against reinfection with SARS-CoV-2, and if so, what concentration of antibodies is needed to confer protection."
*Taken from: Information for Laboratories about Coronavirus (COVID-19)
The opinion comes from a leading researcher that is not in the U.S.
The issue with the CDC is that it has lost a lot of credibility with the ridiculous early claim that masks were ineffective. It turns out they made that claim because they wanted more masks for essential workers in health care, but they knew the claim was bullshit from the beginning. So, unfortunately it means many people won’t trust what they say.
I am not saying they’re wrong about immunity, though a careful read of that statement you quoted basically leads to the conclusion that they simply don’t know for sure one way or another.
Since we just recovered and have a weakened immune system, we will continue to be careful to protect ourselves and others. I trust my source more than the CDC.