This claim is directly contradicted in the paper you linked:
> The effectiveness of previous infection alone against symptomatic BA.2 infection was 46.1% (95% confidence interval [CI], 39.5 to 51.9).
...
> The effectiveness of three doses of BNT162b2 and no previous infection was 52.2% (95% CI, 48.1 to 55.9).
GP is citing a part of the paper where they show...that natural infection is statistically indistinguishable from 3 doses. QED.