Yes, the vaccine can mitigate symptoms and help prevent serious illness; however, that wasn't the point. The point was that it's incorrect to think the vax'd can't catch and spread the virus.
LITTLE SCIENTIFIC PROOF FOR THIS: Everybody can get it now and spread it, but if you are vaxxed and boosted you have better odds against getting it and spreading it.
Studies go both ways, and few are yet peer reviewed. Causal observation show infections at all time high, when vaccines are at high also.