Does catching Covid give you more immunity than being vaccinated?

Immunity to Covid-19. We've all been hoping to develop it ever since the virus emerged two years ago. Since then, a race to vaccinate the world has begun in earnest, with many countries rolling out booster shots in response to the rise of the Omicron variant. Health officials and scientists agree that vaccines are the safest way to develop immunity to the disease. But when US Congresswoman Nancy Mace took to Fox News recently, citing a study showing a whooping 27 times better immunity from natural infection than vaccination, we thought we'd better investigate. How did this study arrive at this number, and is it a fair representation of its findings?