What I don't quite get is why it's being said (all

What I don't quite get is why it's being said (all around the world), that those vaccinated are less likely getting infected. It makes no sense. The virus won't drop off and die immediately as if it just touched an electric fence. A vaccinated immune system will hopefully react in a fast way, that's it, nothing more, nothing less. And during that time the - asymptomatic - vaccinated person is spreading the virus unknowingly, just as an asymptomatic unvaccinated person would.
I suspect somehow methodological mistakes. Who are the ones being tested and to what proportions? Is it statistically representative?