It's a common myth repeated by everyone, everywhere. But it's not true. It came from a reasonable source, the vaccine trials. But the number of breakthrough infections in the trials were tiny, dozens. The fact that none or few of them were severe had no statistical significance. The same claim was repeated for all the trials but all of them had the same problem, small numbers.
Actual data: 5,000 breakthrough cases in Mass. 80 deaths, 1.6% mortality. No difference from the unvaccinated cases.
Um, wouldn't that depend on whether the "proclamation" was made before or after symptoms developed?
It DOES make sense that if Covid has gotten far enough ahead of one's immune system that the battle makes one feel sick, the course of the disease thereafter will not likely differ much from an unvaccinated person to one vaccinated. The invasion has beaten the quick response shoreline defense... (A poor analogy, but the best I can come up with at this hour.)