The CDC report that 2.3x number is based off of was bogus science and it's been debunked repeatedly: https://www.powerlineblog.com/archives/2021/08/more-voodoo-e...

TLDR: The CDC is dishonest and cherry-picks data to meet their narrative. Multiple peer-reviewed studies have shown natural immunity to work at least as well as vaccine immunity for COVID.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8209951/pdf/RMV...

https://www.cell.com/cell-reports-medicine/fulltext/S2666-37...

https://www.thelancet.com/action/showPdf?pii=S2589-5370(21)0...

https://jamanetwork.com/journals/jama/fullarticle/2781112