You are correct. From a purely epidemiological standpoint, there are two problems though:

A. They don't know if any of the current vaccines prevent infection with SARS-CoV-2. What they do know is that those who reveiced the vaccine are less likely to die from Covid-19. They don't know if those people are less likely to contract SARS-CoV-2, or have an asymptomatic infection, or get Covid-19 in a more moderate form (not leading to death). On this note: people who received vaccines such as BCG in the past are significantly less likely to run into any problems with SARS-CoV-2, anyway. So there might be some underlying immunological mechanism there that does not have anything to do with the SARS-CoV-2 vaccine specifically.

B. Since they don't know if those who received the SARS-CoV-2 vaccine can or cannot contract a SARS-CoV-2 infection, as outlined in point A., they also don't know if those people do not continue to spread the virus. (E.g. if the vaccine merely lessens the symptoms of an infection you'll end up with more asymptomatically infected people who spread the virus far wider than symptomatic ones).