Not hearing so much about people who have natural immunity and have had a breakthru infection.
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Appears to be an example that confirms your statement:
Natural infection vs vaccination: Which gives more protection?
Nearly 40% of new COVID patients were vaccinated - compared to just 1% who had been infected previously.
https://www.israelnationalnews.com/News/News.aspx/309762
Also, has anyone been confirmed to have been infected three times?