Vaccinated people don't universally think they are safe. Many of us take precautions such as masking and distancing. I wear a face shield if I have to go into a store or doctor's office.

Vaccines cut down on the number of infections, period. People who also take precautions also cut down on the number of infections. If more people were vaccinated, there would be fewer infections, and fewer opportunities for the virus to mutate.

I can't imagine why anyone would want to claim that not to be true.